Trains. Please help!

Question

The difference in the average speed of two trains is 16 miles per hour. The slower train takes 2 hours longer to travel 170 miles than the faster train takes to travel 150 miles. Find the speed of the slower train.

Answer 1

If this were a question on a speed test, or at least one where budgeting time is important, such as SAT and ACT, here's what I would do.

I answered this in just a few seconds without solving any equations.

First, get the Big Picture.  From the numbers given, there aren't any fractions involved.

So I look at 150 miles for the faster train.

50(mph) goes into it 3 time (3 hours) - which would mean 5 hours for the slower train.

5(hours) goes into 170(miles) 34 times, a difference of 16mph from 50mph.  Bingo!

This is how I teach SAT & ACT math prep.

In retrospect -

factors of 150: 15, 30, 50, 75

factors of 170: 17, 34, 85.  Where's a difference of 16?

 

 

 

 

 

Answer 2

Set up your equations starting with the distance formula: distance = velocity x time

 

There are two distance equations. We'll use X1, V1, and T1 for the slower train,

and X2, V2, and T2 for the faster train.

 

Translating the word problem into equations:

 

V1 x T1 = 170

 

V2 x T2 = 150

 

V2 - V1 = 16

 

T1 - T2 = 2

 

Use substitution, working toward an equation with only V1 as a variable.

 

This should be quadratic, with one solution calculating negative times (not valid),

and the other solution giving positive times for the two trains.

 

Using the calculated V1, calculate the other variables using all the original equations as a check.