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 bin 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

Answer:

Step-by-step explanation:

Let x = speed of the faster runner

Let y = speed of the slower

:

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 the two equations

x - y = 2

x + y = 16

-------------addition eliminates y, find x

2x = 18

x = 9 mph 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

1(9 + 6) = 16