A cyclist bikes at a constant speed for 21 miles . He then returns home at the same speed but takes a different route. His return trip takes one hour longer and is 26 miles. find the speed.

Question

A cyclist bikes at a constant speed for 21 miles . He then returns home at the same speed but takes a different route. His return trip takes one hour longer and is 26 miles.  find the speed.

anonymous · Answer

(21/x)=(26/(x+1))
Solve for X

anonymous · Answer

I don't agree with this...  Well, the equation is correct, but when you solve for x you are finding the time not the speed.

anonymous · Answer

speed = distance/time
since the speed is constant, you set the speeds the same
21/x is the speed there and 26/(x+1) is the speed returning

anonymous · Answer

When you solve for x you get 
21x + 21 = 26x
21  = 5x
x = 4.2   this is time in hours.

Substitute back in    r = 21/x   and r = 26/(t + 1)
so rate = 21/4.2 = 5 mph    and 26/(4.2+1) = 5 mph

anonymous · Answer

I agree you set the speed equal to each other, but the X represents the time in the equation not the rate.

d = rt
21 = rt    and 26 = r(t+1)    solve for r    r = 21/t   and   r = 26/(t+1)   

Set them equal, but you are solving for t   which is time.....

anonymous · Answer

ahh...yea, my bad.  You right