Question

Two runners start from the same point at the same time.They will be 4 miles apart at the end of two hours if running in the same direction and they will be 16 miles apart at the end of one hour if running in opposite directions. Find their speeds?

Answer 1

Step-by-step explanation:

let x= the speed of the faster runner

let y= the speed of the slower runner

write a distance equation for each scenario

2(x - y) = 4; running the same direction

simplify, divide by 2

x - y = 2

and

1(x+y) = 16 ; running opposite directions.

add two equations

x - y =2

x + y = 16

addition eliminates y, find x

2 x=18

x = 9mph is the Faster runner

then

9 + y =16

y= 16-9

y= 7 mph is the slower runner

check solution in the two equations

2(9 - 7) = 4

and

9+y=16

y= 16-9

y=7mph is the slower runner

check solution in the two equations

2(9-7)= 4

1(9+6)= 16