How would you set this equation up?
Every weekended, you ride your bicycle on the river bike trail to veil falls, 16 miles form your house. One weekend, you notice that because the ride to the waterfall partially uphill, you cycling speed returning is 4 miles per hour faster than the speed of riding to the waterfall. If the round trip takes 1 hour and 48 minutes, find the average speed cycling back from the waterfall that ends at veil falls.

Question

How would you set this equation up? 
Every weekended, you ride your bicycle on the river bike trail to veil falls, 16 miles form your house. One weekend, you notice that because the ride to the waterfall partially uphill, you cycling speed returning is 4 miles per hour faster than the speed of riding to the waterfall. If the round trip takes 1 hour and 48 minutes, find the average speed cycling back from the waterfall that ends at veil falls.

anonymous · Answer

The total distance that you travel is 32 miles. in 1.8 hours.
so your speed, v, is related to that by v = d/t = 32/1.8

but also v = (u2 + u1)/2 to get average velocity. where u2 is returning speed and u1 is going. and u1+4 = u2 since returning speed is faster than going. 

If you put all those together
u1+4 + u1 = v = 32/1.8 where u1 is the only unknown.

u1 = 15.778 mi/hr = going speed
u2 = 19.778 mi/hr = returning speed.