# Math Competition Problems Problem of the Week - 5

Updated: Apr 13, 2018

##### Jeremy's father drives him to school in rush hour traffic in 20 minutes. One day there is no traffic, so his father can drive him 18 miles per hour faster and gets him to school in 12 minutes. How far in miles is it to school?

##### Source: AMC8 2015

Oh good. Another distance-time-speed question :) The one that always troubles all middle schoolers and probably some high-schoolers too!

So this question has 2 scenarios. One with traffic and another without. So let’s do a table for both scenarios. We need to see how they both relate to each other. That’ll help us solve the question so much faster.

**Distance = Speed * Time**

D1 = S * 20/60

D2 = (S+18) * 12/60

Since D1 = D2 (They are travelling the same distance from home to school)

S * 20/60 = (S+18) * 12/60

Multiplying both sides by 60 we get

20S = 12S + 216

8S = 216

**S = 27**

Now that we found that S = 27 miles/ hr, let’s plug it back to the first equation

D1 = S * 20/60 to get our distance

D1 = 27 * 20/60

= 27 *1/3

= 9 miles

**So it is 9 miles to school**

Summary - if you get a distance-time-speed question with 2 scenarios, always make a table to see how the scenario variables relate to each other. It makes the problem so much more easy to solve

**Now you try a similar problem**

A cargo plane flew to the maintenance facility and back. It took one hour less time to get there than it did to get back. The average speed on the trip there was 220 mph. The average speed on the way back was 200 mph. How many hours did the trip there take?

**Post the answer to the problem in the comments section below. **

The person who gets it right 5 times in a row will win a free 30 min one-on-one problem-solving session. So get your answers in now! Let's see who wins

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