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Question 428263: lois and clark, two elderly reporters are covering separate stories and have to travel in opposite directions. lois leaves the daily planet building at 0800 am
and travels at 35 mph. clark leaves at 0815 and travels at 40 mph. at what time will they be 140 mi apart?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! they are traveling in opposite directions.
the total distance both of them have to travel is 140 miles.
since they are traveling in opposite directions, their miles traveled will be additive.
lois leave at 0800 and travels at 35 miles per hour.
clark leaves at 0815 and travels 40 miles per hour.
in 15 minutes, lois will have traveled 1/4 of an hour at 35 miles per hour for a distance of 8.75 miles.
since they are already 8.75 miles apart, they have a remaining 131.25 miles to travel in order to be a total of 140 miles apart.
the time they have to travel needs to be the same from 0815 on.
we'll call that T.
lois will be traveling for a total of 35 miles per hour for T hours.
clark will be traveling for a total of 40 miles per hour for the same T hours.
the formula to be used will be:
35 * T + 40 * T = 131.25
combine like terms to get 75 * T = 131.75
divide both sides of the equation by 75 to get T = 131.75 / 75.
this makes T equal to 1.75 hours.
in 1.75 hours, lois will have traveled 35 * 1.75 equals 61.25 miles.
in 1.75 hours, clark will have traveled 40 * 1.75 equals 70 miles.
the total distance traveled is 131.25 miles.
since they were already 8.75 miles apart at 0815, then they are now 140 miles apart.
1.75 hours is equal to 1 hour and 45 minutes.
add 1 hour and 45 minutes to 8 hours and 15 minutes and you get 10 hours and 0 minutes which is equal to 1000 hours or 10:00 am.
a distance and time line would probably something look like this:
0800 0815
A----->B
8.75
1000 0815 1000
D<-------------------------A B-------------------->C
70 miles 61.25 miles
At 0800 lois leaves point A and travels to point B for a distance of 8.75 miles.
At 0815 Lois leaves point B and travels to point C for a distance of 61.25 miles.
At 0815 Clark leaves point A and travles to point D for a distance of 70 miles.
Total distance traveled by Lois is 61.25 + 8.75 = 70 miles.
Total distance traveled by Clark is 70 miles.
Total distance between Lois and Clark is 140 miles.
Time traveled is .25 hours from 0800 to 0815 plus 1.75 hours from 0815 to 1000.
they are 140 miles apart at 1000 hours or 10:00 am.
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