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.
let d = distance to work
Write a time equation: time = dist/speed
:
to work time + return time = 1.5 hrs
{{{d/7}}} + {{{d/12}}} = 1.5
multiply by 84 to get rid of the denominators
84*{{{d/7}}} + 84*{{{d/12}}} = 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/50}}} + {{{d/20}}} = 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