SOLUTION: Olivia lives thirty-two miles from work. This morning, she left for work at 8:43 a.m. There was construction for the first twenty miles, so Olivia only drove at an average speed of

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Question 316841: Olivia lives thirty-two miles from work. This morning, she left for work at 8:43 a.m. There was construction for the first twenty miles, so Olivia only drove at an average speed of seventeen mph around the construction area. If Olivia needs to be at work by 10:11 a.m., what should be her average speed for the rest of the way to work?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Olivia lives thirty-two miles from work.
This morning, she left for work at 8:43 a.m.
There was construction for the first twenty miles, so Olivia only drove at an
average speed of seventeen mph around the construction area.
If Olivia needs to be at work by 10:11 a.m., what should be her average speed
for the rest of the way to work?
:
Summarize what we know about this
1st 20 mi, 17 mph
last 12 mi, drove at a higher speed (s)
:
total time to make the trip: 10:11 - 8:43 = 1:28 min or 1.47 hrs
:
Write a time equation: time = dist/speed
slow time + fast time = total time
20%2F17 + 12%2Fs = 1.47
multiply by 17s, results
20s + 17(12) = 17s(1.47}
20s + 204 = 24.99s
204 = 24.99s - 20s
204 = 4.99s
s = 204%2F4.99
s = 40.88 ~ 41 mph speed on the last 12 mi
:
:
See if that's true, find the times
20/17 = 1.1765 hrs
12/41 = .29 hrs
-------------------
total: 1.469 ~ 1.47 hrs