What is the equation

Question

Denise has 3 hours to spend training for an upcoming race.she completes her training by running full speed the distance of the race and walking back the same distance to cool down. If she runs at the speed of 8 mph and walks back at a speed of 2 mph, how long should she plan to spend walking back ?

Answer 1

Off the bat, we know that if she ran 1 hour out she would have to walk 4 hours back which is over the time since Denise only gets 3 hours.

There are two equations:

1) time

a + b = 3hrs (total time)

a = time she went running

b = time she spends walking back

2) distance

d * 8mph * a = d * 2mph * b

d = distance ( which cancels out)

You're looking for the time she is needs to walk back, so solve for "b" in the distance equation (distance cancels out).

8 * a = 2 * b

Can't solve for "b" if "a" is there, so using the time equation (do some algebra):

a = 3 - b

Plug in:

8 * (3 - b) = 2 * b

find b