SOLUTION: Stephanie and her friend, Paula, are waiting for a shuttle to take them to their terminal at the airport. The first shuttle that arrives only has room for one more passenger, so

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Question 633896: Stephanie and her friend, Paula, are waiting for a shuttle to take them to their terminal at the airport. The first shuttle that arrives only has room for one more passenger, so Stephanie gets on. The next shuttle arrives 10 minutes later and Paula gets on. If Stephanie's shuttle travels at a speed of 20 mph and Paula's shuttle travels at a speed of 35 mph, how long will it take Paula's shuttle to catch up to Stephanie's shuttle?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The first shuttle that arrives only has room for one more passenger, so
Stephanie gets on.
The next shuttle arrives 10 minutes later and Paula gets on.
If Stephanie's shuttle travels at a speed of 20 mph and Paula's shuttle travel
at a speed of 35 mph, how long will it take Paula's shuttle to catch up to
Stephanie's shuttle?
:
When the 2nd shuttle (35mph) catches the 1st (20mph) they will have traveled
the same distance
:
Change 10 min to 1%2F6 hrs
:
Let t = travel time of the 2nd shuttle
then
(t+1%2F6) = travel time of the 1st shuttle
:
Write a distance equation, dist = speed * time
35t = 20(t+1%2F6)
35t = 20t + 20%2F6
35t - 20t = 20%2F6
15t = 20%2F6
multiply both sides by 6
6(15t) = 20
90t = 20
t = 20%2F90
t = 2%2F9 * 60 = 131%2F3 minutes for the 2nd shuttle to catch the 1st.