Adam decides to travel from City A to City B at a uniform speed and re

Question

Adam decides to travel from City A to City B at a uniform speed and reach City B after T hours. After 30 miles, as a result of an engine malfunction, the speed of the car becomes \(\frac{4}{5}\)th of the original speed. Therefore, he travels the rest of the distance at a constant speed \(\frac{4}{5}\)th of the original speed and reaches City B 45 minutes late. Had the engine malfunction happened after he traveled 48 miles, he would have reached only 36 minutes late. What is the distance between City A and City B?

A. 20 miles
B. 40 miles
C. 90 miles
D. 120 miles
E. 150 miles

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Official Answer

D

A. 20 miles
B. 40 miles
C. 90 miles
D. 120 miles
E. 150 miles

Are You Up For the Challenge: 700 Level Questions

rsrighosh · Answer

Can anybody share their method. Mine involved too many calculations.

satyam1010 · Answer

speed reduction is 1/5 so time increase will be 1/4, in 1st case the time will be 1/4 of x = 45 min ,so total time is 180 min .; 3 hours , now he travelled 18 miles in 1/4 of 9 min so time will be 36 min , so speed will be .5 miles/hour so distanceis .5*180=90

satyam1010 · Answer

speed reduction is 1/5 so time increase will be 1/4, in 1st case the time will be 1/4 of x = 45 min ,so total time is 180 min .; 3 hours , now he travelled 18 miles in 1/4 of 9 min so time will be 36 min , so speed will be .5 miles/hour so distanceis .5*180=90

emsgmat · Answer

Hi all,

I'm a new member and am going to take the GMAT in a few days. Based on my solution, answer should be  D  (120 mi).

Let d = distance between City A and City B
, t = time (in minutes) 
, r = rate

Step 1: Create equation for first condition (after 30 mi):

d/r + d-30/4/5r = t+45

Step 2: Create equation for second condition (after 48 mi):

d/r + d-48/4/5r = t+36

Step 3: Form a ratio based on equations:

d-48/d-30 = 36/45

d = 120

Hope it's clear and concise. Let's stay tuned for the OA from Bunuel. Thanks for posting the question btw!

Cheers

thecardinal · Answer

Here is a solution:

First Scenario:
A-----------|---------------------B

Second Scenario:
A--------------------|------------B

The difference in time for the two Scenarios is due to the unequal segment in which:
distance = 48-30 = 18 miles
difference in time = 9 min
so we have the equation
18/ (4/5) r - 18/r = 9
r=0.5 miles/minute

Now you take one of two scenarios and you ask:
(let's take scenario 1)
r=0.5 miles/minute r' = 0.4 miles/minute

Ask yourself how many miles I should travel to do +45 minutes with r'
(You can see 0.5 miles/minute as 4 minutes to do 2 miles and 0.4 miles/ minute as 5 minutes to do 2 miles)
So you do (5/2 - 4/2)*(d-30)=45 d=120 (d-30 because you did 30 miles before breakdown)

That's All Folks!

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