SOLUTION: Alice borrowed a bicycle from her friend, Bob, and wanted to return it. She rode the bicycle from her house to Bob's house at 7 miles per hour. She jogged back home from Bob's hous
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Question 268135: Alice borrowed a bicycle from her friend, Bob, and wanted to return it. She rode the bicycle from her house to Bob's house at 7 miles per hour. She jogged back home from Bob's house to her house at a pace of 5 miles per hour. It took Alice 36 minutes (i.e., 3/5 hour) total travel time to make her round trip.
(a) How long (in minutes) did each leg of Alice’s trip take? That is, how long did it take Alice to travel to Bob’s house? How long did it take Alice to travel home from Bob’s house?
(b) What is the distance between Alice's and Bob's houses?
You can put this solution on YOUR website! She rode the bicycle from her house to Bob's house at 7 miles per hour.
She jogged back home from Bob's house to her house at a pace of 5 miles per hour.
It took Alice 36 minutes (i.e., 3/5 hour) total travel time to make her round trip.
:
36 min =.6 hr
(a) How long (in minutes) did each leg of Alice’s trip take?
That is, how long did it take Alice to travel to Bob’s house?
How long did it take Alice to travel home from Bob’s house?
:
Let t = time (in hrs) to travel to Bob's house
then
(.6-t) = time to travel from his house
:
Dist both ways is the same; write a dist equation: dist = speed * time
To dist = From dist
7t = 5(.6-t)
7t = 3 - 5t
7t + 5t = 3
12t = 3
t =
t = .25 hrs; that is .25(60) = 15 min to
and
.6-.25 = .35; that is .35(60) = 21 min from
:
:
(b) What is the distance between Alice's and Bob's houses?
:
.25(7) = 1.75 mi
check it using the return time and speed
.35(5) = 1.75 mi
