how far is it from the park to the cyclist's house?

Question

It takes a bicyclist a total of nine hours to travel from his house to the park and back home. If he travels 28 mph on the way to the park and 14 mph on the return trip, how far is it from the park to the cyclist's house?

Answer 1

Ah, you posted a sly one! Still, we can nail this critter!

we already know the speeds the cyclist travels, so finding the distance requires only that we find the times traveled each way. How do the times relate? 

X = outgoing time (in hours)

Y = returning time (also in hours)

They total 9, so we get:

 X + Y = 9

We know the two distances are equal, whether leaving or returning. That means riding at 28 mph for X hours is the same as riding at 14 mph for Y hours. In other words:

28X = 14Y             Simply solve for Y:

28X / 14 = 14Y / 14

2X  = Y

Plug that back into the time equation:

 X + 2X = 9

 3X  = 9

3X / 3 = 9 / 3

X = 3

And since Y = 2X

Y = 2(3) = 6

That means our cyclist rode at 28 mph for 3 hours, or 84 miles total. Likewise, the return trip was 14 mph for 6 hours, so again 84 miles. 

84 + 84 = 168 miles