Answer:
10/3 mph
Step-by-step explanation:
Obviously, (time going) + (time returning) = (total time spent en route) = 54 min. Since time = distance / rate,
3 miles 3 miles
----------------------- + --------------------- = 54 min
downhill speed uphill speed
Let u = uphill speed and d = downhill speed; then d = u + 5 (all in mph)
Then we have:
3 miles 3 miles
----------------------- + --------------------- = 54 min
u + 5 u
and our task here is to determine the uphill speed, u.
The LCD is u(u + 5). Thus we have:
3u 3(u + 5) miles
----------------------- + ----------------------- = 54 min = 0.9 hr
u(u + 5) u(u + 5)
so that:
6u + 15
----------------------- = 0.9 hr or 6u + 15 = 0.9(u)(u + 5), or
u(u + 5)
6u + 15 = 0.9u² + 4.5u
Combining the u terms, we get:
15 = 0.9u² + 4.5u, or 0.9u² + 1.5u - 15 = 0
Eliminating the fractions, we get 9u² + 15u - 150, or
3u^2 + 5u - 50 = 0
This factors into (3u - 10)(u + 5) = 0. The only positive root is u = 10/3.
Your average rate on the return trip (uphill) is 10/3 mph (3 1/3 mph).
