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A truck left City M and traveled toward City N. A second truck left

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nick13
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A truck left City M and traveled toward City N. A second truck left [#permalink] A truck left City M and traveled toward City N. A second truck left   22 Oct 2023, 16:40
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A truck left City M and traveled toward City N. A second truck left City N exactly 1 hour later and traveled toward City M. The trucks passed each other after they had traveled, nonstop, a combined total of 490 miles. If the average speeds of the trucks up to the time they passed each other were 50 miles per hour (mph) and 60 mph, respectively, how far, to the nearest mile, had the first truck traveled when the trucks passed each other?

A. 223
B. 240
C. 245
D. 250
E. 300

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gmatophobia
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Re: A truck left City M and traveled toward City N. A second truck left [#permalink] A truck left City M and traveled toward City N. A second truck left   22 Oct 2023, 18:58
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nick13 wrote:
A truck left City M and traveled toward City N. A second truck left City N exactly 1 hour later and traveled toward City M. The trucks passed each other after they had traveled, nonstop, a combined total of 490 miles. If the average speeds of the trucks up to the time they passed each other were 50 miles per hour (mph) and 60 mph, respectively, how far, to the nearest mile, had the first truck traveled when the trucks passed each other?

a. 223
b. 240
c. 245
d. 250
e. 300


Let's assume that the speed of the first truck (\(s_1\)) = 50 mph

The speed of the second truck (\(s_2\))= 60 mph

Distance covered by the first truck when the second truck begins its journey = 50 miles

Remaining distance = 490 - 50 = 440 miles

The ratio of the distance covered by the two trucks is in the ratio of their speeds

\(\frac{s_1}{s_2} = \frac{50}{60} = \frac{5}{6}\)

Hence, out of the 11 parts of the journey, the second truck covers 6 parts, and the first truck covers 5 parts.

Distance covered by the first truck = \(\frac{440}{11} * 5 = 200\)

Total distance covered = \(200 + 50 = 250\)

Option D
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Re: A truck left City M and traveled toward City N. A second truck left [#permalink] A truck left City M and traveled toward City N. A second truck left   30 Mar 2024, 21:57
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nick13 wrote:
A truck left City M and traveled toward City N. A second truck left City N exactly 1 hour later and traveled toward City M. The trucks passed each other after they had traveled, nonstop, a combined total of 490 miles. If the average speeds of the trucks up to the time they passed each other were 50 miles per hour (mph) and 60 mph, respectively, how far, to the nearest mile, had the first truck traveled when the trucks passed each other?

A. 223
B. 240
C. 245
D. 250
E. 300

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Attachment:
Truck.png

­Truck 1 Distance: R x T --- > 50 x (t + 1) = 50t + 50
Truck 2 Distance: R x T --- > 60t

Combined Distance of both trucks = 50t +50 + 60t = 490 miles
110t + 50 = 490 
110t = 440
t = 4

Distance of truck 1: 50(4) + 50 = 200 +50 = 250 miles 

Option D­
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Re: A truck left City M and traveled toward City N. A second truck left [#permalink] A truck left City M and traveled toward City N. A second truck left   07 Apr 2024, 04:14
the first truck has traveled one more hour than the second at the time two trucks pass each other

­\(\frac{x}{50} - 1 = \frac{490 - x}{60}\)­

­\(x = 250\)­
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A truck left City M and traveled toward City N. A second truck left [#permalink] A truck left City M and traveled toward City N. A second truck left   19 May 2024, 09:52
I understood the solution. But I have a doubt in this.
The question doesn't say that the trucks are travelling at the constant speed.
Infact, question mentions the AVERAGE speed till the time trucks pass each other.

In this case, is it correct to assume that Truck 1 covered 50 miles in first hour of its journey?­
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Re: A truck left City M and traveled toward City N. A second truck left [#permalink] A truck left City M and traveled toward City N. A second truck left   19 May 2024, 11:22
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T4Star wrote:
A truck left City M and traveled toward City N. A second truck left City N exactly 1 hour later and traveled toward City M. The trucks passed each other after they had traveled, nonstop, a combined total of 490 miles. If the average speeds of the trucks up to the time they passed each other were 50 miles per hour (mph) and 60 mph, respectively, how far, to the nearest mile, had the first truck traveled when the trucks passed each other?

A. 223
B. 240
C. 245
D. 250
E. 300

I understood the solution. But I have a doubt in this.
The question doesn't say that the trucks are travelling at the constant speed.
Infact, question mentions the AVERAGE speed till the time trucks pass each other.

In this case, is it correct to assume that Truck 1 covered 50 miles in first hour of its journey?­

­
No, assuming that the truck from City M covered 50 miles in the first hour isn't necessarily correct. The question specifies the average speed, not the constant speed. However, you can set up the equation 50t + 60(t - 1) = 490 without needing to split the distances covered in the first hour and the rest of the time. Having said that, in this particular question, assuming a constant speed would still yield the correct result.
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Re: A truck left City M and traveled toward City N. A second truck left [#permalink] A truck left City M and traveled toward City N. A second truck left   19 May 2024, 18:28
Since in this question, we can take average speed to be equal to constant speed, here is how I did it.

In the first hour, first truck will travel 50 miles.
Total miles remaining = 490 - 50 = 440

Combined speed = 110

Time travelled = 440/110 = 4 hours.

First truck has travelled for 4 + 1 = 5 hours.

Distance travelled = 50*5 = 250 miles.
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Re: A truck left City M and traveled toward City N. A second truck left [#permalink]
19 May 2024, 18:28
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