SOLUTION: A woman hikes to the bottom of the Grand Canyon at a rate of 4.5 mph and returns to the top by mule at a rate of 2.5 mph. If the total time of the trip is 7 hours, how lond did she

Question 272177: A woman hikes to the bottom of the Grand Canyon at a rate of 4.5 mph and returns to the top by mule at a rate of 2.5 mph. If the total time of the trip is 7 hours, how lond did she walk and what was the total length of her trip?
Let= statement and formula please. Thank You.
Found 2 solutions by oberobic, stanbon:
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
d=rt, where d=distance, r=rate, and t=time
t = d/r= 7
so
x = time walking down @ 4.5 mph
7-x = time walking up @ 2.5 mph
.
total time = 7 = time walking down + time walking up
.
4.5(x) = d = distance walking down
2.5(7-x) = d = distance walking up, which has to equal distance walking down
.
4.5x = 2.5(7-x) = 17.5 - 2.5x
adding 2.5x to both sides
7x = 17.5
x = 2.5 hr
7-x = 7 - 2.5 = 4.5 hr
.
so, she walks down for 2.5 hr at a pace of 4.5 mph = 11.25 miles
and
she walks up for 4.5 hr at a pace of 2.5 = 11.25 miles
.
so the total length of the trip was 11.25 + 11.25 = 22.5 miles
.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A woman hikes to the bottom of the Grand Canyon at a rate of 4.5 mph and returns to the top by mule at a rate of 2.5 mph. If the total time of the trip is 7 hours, how long did she walk and what was the total length of her trip?
-----------------------
Down DATA:
rate = 4.5 mph ; distance = x miles ; time = x/4.5 hrs
--------------------
Up DATA:
rate = 2.5 mph ; distance = x miles ; time = x/2.5 hrs
--------------------
Equation:
time + time = 7 hrs
x/(9/2) + x/(5/2) = 7
Multiply thru by 45 to get:
10x + 18x = 45*7
28x = 45*7
4x = 45
x = 45/4 miles = 11 1/4 miles (length of her trip)
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Walking time = (45/4)/(9/2) = (45/4)(2/9) = 5/2 = 2.5 hrs
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Cheers,
Stan H.
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