SOLUTION: Mr. Thimas drove his old truck to the city at a rate of 40mi/hr and drove back home on the interstate at 60mi/hr. The total trip took 6 hours. How far is Mr. Thomas's home from the

Question 1188476: Mr. Thimas drove his old truck to the city at a rate of 40mi/hr and drove back home on the interstate at 60mi/hr. The total trip took 6 hours. How far is Mr. Thomas's home from the city
Found 3 solutions by ikleyn, Alan3354, greenestamps:
Answer by ikleyn(52817)   (Show Source): You can put this solution on YOUR website!
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Mr. Thimas drove his old truck to the city at a rate of 40mi/hr and drove back home
on the interstate at 60mi/hr. The total trip took 6 hours.
How far is Mr. Thomas's home from the city
~~~~~~~~~~~~~~

Let d be one way distance (which is the unknown value under the problem's question). Write the total time equation + = 6 hours. To solve it, multiply both sides by 120. You will get 3d + 2d = 6*120 5d = 720 d = 720/5 = 144 miles. ANSWER. The distance is 144 miles.

Solved (and corrected).

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Mr. Thimas drove his old truck to the city at a rate of 40mi/hr and drove back home on the interstate at 60mi/hr. The total trip took 6 hours. How far is Mr. Thomas's home from the city
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Avg speed = 2*40*60/(40+60) = 48 mi/hr
6*48 = 288 miles RT, 144 miles each way

Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!

The first tutor used a standard formal algebraic solution method but used the wrong total travel time; I'm sure she will see this note and fix her response.

The second tutor used a magic formula which is well worth remembering, since it appears in a large number of similar problems:

The average speed for traveling from A to B and back at speeds of x and y is

Here is another informal way to solve the problem quickly, if formal algebra is not required.

The ratio of the two speeds is 40:60 = 2:3, and the distances are the same, so the ratio of times at the two speeds is 3:2.

So 3/5 of the total travel time of 6 hours was at 40mph, and 2/5 was at 60mph. Using either of those facts gives the distance:

3/5 of 6 hours at 40mph: (3/5)(6)(40) = 144 miles
2/5 of 6 hours at 60mph: (2/5)(6)(60) = 144 miles

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