SOLUTION: Mark rode his new Harley 60 mph for part of the trip and 70 mph for the rest of the trip home from the Shakespeare Festival in Ashland Oregon. If the entire trip was 250 miles an

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Question 1109159: Mark rode his new Harley 60 mph for part of the trip and 70 mph for the rest of the trip home from the Shakespeare Festival in Ashland Oregon. If the entire trip was 250 miles and he spent twice as much time traveling at a faster speed, how many miles would he be able to travel at each rate?
Found 2 solutions by ikleyn, ankor@dixie-net.com:
Answer by ikleyn(52884) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let "t" be the time he rode at 60 mph.

Then the time he rode at 70 mph wa 2t.



The "distance equation is 

    60*t + 70*(2t) = 250     miles,     or


60t + 140t = 250  ====>  200t = 250  ====>  t = 250%2F200 = 5%2F4.


Thus he rode  t = 5%2F4 of an hour = 1 hour 15 minutes at  60 mph.


Then he rode  2t = 2 hours and 30 minutes at 70 mph.

Solved.

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Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Mark rode his new Harley 60 mph for part of the trip and 70 mph for the rest of the trip home from the Shakespeare Festival in Ashland Oregon.
If the entire trip was 250 miles and he spent twice as much time traveling at a faster speed, how many miles would he be able to travel at each rate?
:
let d = distance traveled at 70 mph
The total distance is given at 250 mi, therefore:
(250-d) = distance traveled at 60 mph
:
Write a time equation; time = dist/speed
70mph time = twice 60mph time
d%2F70 = 2*%28%28250-d%29%2F60%29
we can cancel the 2
d%2F70 = %28%28250-d%29%2F30%29
multiply both sides by 210, cancel the denominators
3d = 7(250-d)
3d = 1750 - 7d
3d + 7d = 1750
10d = 1750
d = 175 mi at 70 mph
then
250 - 175 = 75 mi at 60 mph
:
:
Check by finding the actual time at each speed
75/60 = 1.25 hrs
175/75 = 2.5 hrs, twice as long