Word Problem

Question

2 boys are in a race they both take the same size steps but john takes 14 steps in the time it takes peter to take 9, peter is 60 steps ahead of john before he start to run. How many steps will each runner takes from the time john start running before he catches peter?

Answer 1

Love these kinds of algebraic word problems.  

 

Your equation is as follows:

 

60 + 9x = 14x

 

Peter started at 60 steps and takes 9 steps for x number of times and John takes 14 steps x number of times.  When both sides of the equation are equal then they have both taken the same number of steps and are side by side in the race.

 

If you solve for x you get 12

 

Peter has taken 60 + 9 * 12 steps for a total of 168 steps

 

John has taken 14 * 12 steps for a total of 168 steps

 

Lori

Answer 2

These are both lines.  John's line has a slope of 14.  Peter's line has a slope of 9 and at time zero he's already at 60.

 

14x = 9x+60

5x=60

x=12

 

So at time 12 the lines will cross. 14 * 12 = 168.  They will cross at 168 steps.