IMAT 2016 Q6 [Deliveries]

A delivery company opens its depot at 7:30 am. It uses large and small vans to make deliveries. The smaller vans take 10 minutes to load and then 1 hour to make the deliveries and return. The larger ones have a loading time of 30 minutes and return from deliveries after 2 hours. The driver of a large van starts loading at 8:00 am.

If the driver of a small van is to make the maximum number of deliveries he can, how much later than the driver of the large van can he start loading if they are both to arrive back at the depot for lunch at 1:00 pm?

A. 0 minutes
B. 20 minutes
C. 15 minutes
D. 5 minutes
E. 10 minutes

Simple steps to solve word problems:

  • Underline key information

  • Determine what they are trying to ask, and what you will need to solve it

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  • Solve.

The most difficult part of this question is comprehension. We need to be really clear on what is being asked so we can get the right answer.

The problem gives us 2 different timelines, one for the big van and one for the small. To find the maximum amount of runs, we need to find out how much time is both of their schedules. After this, we can figure out what time the big and small vans start and find their difference.

Note: I will use the 24 hour clock to solve for simplicity.

Small Van:

Between 7:30 and 13:00

Time window for deliveries = Finish time - start time

= 13:00 - 7:30

= 5h30

One run = load time + delivery time

= 00:10 + 1:00

= 1h10

Total runs possible = 5h30 - 1h10 - 1h10 - 1h10 - 1h10

= 00h50

Now we need to work our way back from lunch break at 13:00. It means that you can fit in 5 runs, and so you could start at 7:30 + 00h50 = 8:20 if you wanted to finish exactly at 13:00.

Now for the…

Big Van

Between 8:00 and 13:00

Time window for deliveries = Finish time - start time

= 13:00 - 8:00

= 5h00

One run = load time + delivery time

= 00:30 + 2:00

= 2h30

Total runs possible = 5h00 - 2h30 - 2h30

= 0h00

Now we need to work our way back from lunch break at 13:00. It means that you can fit in 2 runs, and so you could start at 8:00 + 0h00 = 8:00 if you wanted to finish exactly at 13:00.

Finally, find the difference between the two start times:

Small Van: 8:20

Big Van: Small Van: 8:00

The difference between the two is 20 minutes, so the small van driver can start 20 minutes after the large van driver.

\fcolorbox{red}{grey!30}{Therefore B is the answer.}
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