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A taxi service charges $5.50 for the first 1/5th of a mile, $1.50 for

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Bunuel
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A taxi service charges $5.50 for the first 1/5th of a mile, $1.50 for [#permalink] New post   09 Apr 2024, 01:30
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­A taxi service charges $5.50 for the first 1/5th of a mile, $1.50 for each additional 1/5th of a mile, and 20 cents per minute of waiting time. Joan took a cab from her place to a flower shop 8 miles away, where she bought a bouquet, then another 3.6 miles to her mother’s place. The driver had to wait 9 minutes while she bought the bouquet. What was the fare?

A. $20
B. $120.20
C. $92.80
D. $91
E. $90


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Re: A taxi service charges $5.50 for the first 1/5th of a mile, $1.50 for [#permalink] New post   09 Apr 2024, 07:10
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­Waiting Time Cost: \(9*0.2 = 1.8\)

Travelling Cost: As the initial \(\frac{1}{5}\) mile is charged at $5.5, and the remainder of the trip is charged at $1.5 per \(\frac{1}{5}\) mile, we can multiply each of the mile distances by 5 to create a distance-unit which is easy to work with.

Distance to the flower shop: \(8*5 = 40\) \(\frac{1}{5}\)th mile units

Distance to mother's place: \(\frac{36}{10}*5 = 18\) \(\frac{1}{5}\)th mile units

Total \(\frac{1}{5}\)th mile units: \(40+18 = 58\)

Cost: \(5.5 + (1.5*57) = 91\)

Total Cost of Fare: \(1.8 + 91 = 92.8\)

ANSWER C­
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Re: A taxi service charges $5.50 for the first 1/5th of a mile, $1.50 for [#permalink] New post   10 Apr 2024, 03:05
Answer (C)

5.50 + 39 + 19.50 + 18 + 9 + 1.80 = 92.80

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Re: A taxi service charges $5.50 for the first 1/5th of a mile, $1.50 for [#permalink] New post   19 Apr 2024, 01:57
KarishmaB gmatophobia , Can you please provide an easy and innovative solution for this question ? It's getting calculation intensive and big with conventional approach .
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Re: A taxi service charges $5.50 for the first 1/5th of a mile, $1.50 for [#permalink] New post   19 Apr 2024, 06:49
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sayan640 wrote:
KarishmaB gmatophobia , Can you please provide an easy and innovative solution for this question ? It's getting calculation intensive and big with conventional approach .

­A taxi service charges $5.50 for the first 1/5th of a mile

Inference → for the first 0.20 miles, the tax charges = $5.50

$1.50 for each additional 1/5th of a mile

Inference → for the every mile, the tax charges = $7.50

Joan took a cab from her place to a flower shop 8 miles away, where she bought a bouquet, then another 3.6 miles to her mother’s place.

Total Distance = 3.6 + 8 = 11.6

Fare for the extra distance = 11.40 * 7.50 = 85.50

20 cents per minute of waiting time

Waiting Fare = 90 * 2 = $1.80

Total Fare = 85.50 + 5.50 + 1.80 = 92.80

The options are close, else we could have approximated. 
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Re: A taxi service charges $5.50 for the first 1/5th of a mile, $1.50 for [#permalink]
19 Apr 2024, 06:49
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