SOLUTION: 1. The round trip from home to work takes 1.5 hrs. What is the distance to work if the trip going to it was done at 7 miles per hour and the return trip at 12 miles per hour? Verif

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Question 631153: 1. The round trip from home to work takes 1.5 hrs. What is the distance to work if the trip going to it was done at 7 miles per hour and the return trip at 12 miles per hour? Verify.
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2. Bob rows his boat at 50 m/min going downstream and 20 m/min going upstream. How far down the river should he go so that he can return at 3:05pm; from where he started, if he left at 10:45 am? Verify.


If you can help me with these questions it'll be great! I could not find any ways to solve them. Thanks!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
1. The round trip from home to work takes 1.5 hrs.
What is the distance to work if the trip going to it was done at 7 miles per
hour and the return trip at 12 miles per hour? Verify.
let d = distance to work
Write a time equation: time = dist/speed
:
to work time + return time = 1.5 hrs
d%2F7 + d%2F12 = 1.5
multiply by 84 to get rid of the denominators
84*d%2F7 + 84*d%2F12 = 84*1.5
cancel the denominators
12d + 7d = 126
19d = 126
d = 126/19
d = 6.63 mi dist to work
:
verify by finding the times each way
6.63/7 = .947 hrs
6.63/12= .553 hrs
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total time: 1.5 hrs
:
:
2. Bob rows his boat at 50 m/min going downstream and 20 m/min going upstream.
How far down the river should he go so that he can return at 3:05pm; from
where he started, if he left at 10:45 am? Verify.
:
Find the number of minutes from 10:45 am to 3:05 pm
14:65 - 10:45 = 4:20; 4(60) + 20 = 260 minutes downstream and back
:
let d = the one way distance downstream
:
Write a time equation: time = dist/speed
:
Time downstream + time back = 260 min
d%2F50 + d%2F20 = 260
multiply by 100 to get rid of the denominators
2d + 5d = 260 * 100
7d = 26000
d = 26000/7
d = 3,714.3 meters downstream (3.7 km)
:
:
Verify this by finding the time each way
3714.3/50 = 74.3 min
3714.3/20 = 185.7 min
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total time: 260 min