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A bus travelling from city A to city B breaks down midway. After 30 mi 21 Jan 2021, 10:30
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56% (02:54) correct 44% (03:13) wrong based on 133 sessions

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A bus travelling from city A to city B breaks down midway. After 30 minutes, the passengers manage to catch another bus and reach city B on time. Had the breakdown occurred 30 km. earlier, the passengers would have had 37.5 minutes to catch the other bus. If the speed of the second bus is 20 km/hr more than that of the first bus, what is the speed of the first bus, in km/hr ?

A. 82
B. 80
C. 72
D. 60
E. 48


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A bus travelling from city A to city B breaks down midway. After 30 minutes, the passengers manage to catch a taxi and reach city B IN TIME. Had the breakdown occurred 30 km earlier, the passengers would have taken 37.5 minutes to catch the taxi and reach city B IN TIME. If the speed of the taxi is 20 km/hour more than that of the bus, find the speed of the bus in km/hour.
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A bus travelling from city A to city B breaks down midway. After 30 mi 21 Jan 2021, 11:15
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Bunuel
A bus travelling from city A to city B breaks down midway. After 30 minutes, the passengers manage to catch another bus and reach city B on time. Had the breakdown occurred 30 km. earlier, the passengers would have had 37.5 minutes to catch the other bus. If the speed of the second bus is 20 km/hr more than that of the first bus, what is the speed of the first bus, in km/hr ?

A. 82
B. 80
C. 72
D. 60
E. 48

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Let the speed of the buses be x km/hr and x+20 km/hr

From the question stem, it is given that the passengers get 7.5 minutes extra to take the next bus if the breakdown occurs 30 km earlier. The difference in time if the faster bus travels the distance the extra 30 kms is \(\frac{7.5}{60}\) or \(\frac{1}{8}\) hour

The equation formed is \(\frac{30}{x} - \frac{30}{x+20} = \frac{1}{8}\) hour. Simplifying, we will get the equation x(x+20) = 4800.
This will work when the slower bus' speed is 60 km/hr and the faster bus' speed is 80 km/hr.

Therefore, the speed of the first bus in km/hr is 60(Option D)
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A bus travelling from city A to city B breaks down midway. After 30 mi 21 Jan 2021, 12:56
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Given: A bus travelling from city A to city B breaks down midway. After 30 minutes, the passengers manage to catch another bus and reach city B on time. Had the breakdown occurred 30 km. earlier, the passengers would have had 37.5 minutes to catch the other bus.

Asked:If the speed of the second bus is 20 km/hr more than that of the first bus, what is the speed of the first bus, in km/hr ?

Let the speed of the first bus be x km
Speed of the second bus= x+20 km

30/x - 30/(x+20) = 7.5/60 = 1/8
30×20×8 = x(x+20)

60×80=x(x+20)
x=60 kmh

IMO D

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A bus travelling from city A to city B breaks down midway. After 30 mi 21 Jan 2021, 15:04
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Bunuel
A bus travelling from city A to city B breaks down midway. After 30 minutes, the passengers manage to catch another bus and reach city B on time. Had the breakdown occurred 30 km. earlier, the passengers would have had 37.5 minutes to catch the other bus. If the speed of the second bus is 20 km/hr more than that of the first bus, what is the speed of the first bus, in km/hr ?

A. 82
B. 80
C. 72
D. 60
E. 48
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The hypothetical breakdown is 30km earlier than the actual breakdown.
HYPOTHETICAL BREAKDOWN <-----30 km-----> ACTUAL BREAKDOWN

For the case with the HYPOTHETICAL breakdown, the distance above is traveled by the FASTER BUS.
For the case with the ACTUAL breakdown, the distance above is traveled by the SLOWER BUS.
When the faster bus travels the distance above, the rest time between buses = 37.5 minutes.
When the slower bus travels the distance above, the rest time between buses = 30 minutes.
The slower bus reduces the rest time by 1/8 hour.
Implication:
The slower bus requires 1/8 LONGER than the faster bus to travel the 30 km above.

We can PLUG IN THE ANSWERS, which represent the speed of the slower bus.
When the correct answer is plugged in, the slower bus will take 1/8 hour longer than the faster bus to travel 30 km.

B: 80 km per hour for the slower bus, implying 100 km for the faster bus
Time for the faster bus to travel 30 km \(= \frac{distance}{rate} = \frac{30}{100} = \frac{3}{10}\) hour
Time for the slower bus to travel 30 km \(= \frac{distance}{rate} = \frac{30}{80} = \frac{3}{8}\) hour
Time difference \(= \frac{3}{8} - \frac{3}{10} = \frac{15}{40} - \frac{12}{40} = \frac{3}{40}\) hour
Eliminate B.

D: 60 km per hour for the slower bus, implying 80 km for the faster bus
Time for the faster bus to travel 30 km \(= \frac{distance}{rate} = \frac{30}{80} = \frac{3}{8}\) hour
Time for the slower bus to travel 30 km \(= \frac{distance}{rate} = \frac{30}{60} = \frac{1}{2}\) hour
Time difference \(= \frac{1}{2} - \frac{3}{8} = \frac{4}{8} - \frac{3}{8} = \frac{1}{8}\) hour
Success!

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A bus travelling from city A to city B breaks down midway. After 30 mi 06 Sep 2025, 10:28
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Cant we say here that 30Km was covered in 7.5 mins? That is the reason why when the car broke midway, he had only 30 mins to catch the other bus?

Please correct my understanding here?
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A bus travelling from city A to city B breaks down midway. After 30 mi 07 Sep 2025, 03:43
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If there is little time left on the test (~10/20 seconds), and a question like this pops up or you want to just guess and move on, you can choose 60, noticing from answer choices that only 80 and 60 have a difference of 20, and we want to find speed of the slower bus.
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