SOLUTION: Zheng went to the park traveling 6 mph and returned home traveling 4 mph. If the total trip took 5 hours, how long did Zheng travel at each speed?

Question 1195317: Zheng went to the park traveling 6 mph and returned home traveling 4 mph. If the total trip took 5 hours, how long did Zheng travel at each speed?
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!

goingto 6 d/6 d returning 4 d/4 d total 5

Going at 6mph, hours
Returning at 4mph, hours

----------------------earlier try----------------------

SPEEDS TIME DISTANCES GOING 6 RETURN 4 TOTAL 5

SPEEDS TIME DISTANCES GOING 6 x 6x RETURN 4 (5-x) 4(5-x) TOTAL 5

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Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
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Zheng went to the park traveling 6 mph and returned home traveling 4 mph.
If the total trip took 5 hours, how long did Zheng travel at each speed?
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Since each way distance is the same, the traveling time in each direction is inversely proportional to the speed. So, we may think that the time traveling at 6 mph is 4t, while the time traveling at 4 mph is 6t. It gives us the total time equation 4t + 6t = 5 hours, 10t = 5 hours t = 5/10 = 0.5 of an hour, hence, time traveling at the rate 6 mph is 4t = 4*0.5 = 2 hours; time traveling at the rate 4 mph is 6t = 6*0.5 = 3 hours.

Solved MENTALLY.

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

If a formal algebraic solution is required, then you can set the problem up something like what is shown in the response from tutor @josgarithmetic.

But if formal algebra is not needed, a quick mental solution like the one shown in the response from tutor @ikleyn can be used.

(A further note about that.... Solving the problem mentally gives you more good brain exercise than using formal algebra.)

Following is a solution method essentially the same as the one from tutor @ikleyn, presented a bit differently, which might (or might not) be easier to understand.

The distances are the same, so if the ratio of speeds is A:B then the ratio of times is B:A.

The ratio of the two speeds is 6:4 = 3:2, so the ratio of times is 2:3.
A total of 5 hours divided into two parts in the ratio 2:3 is obviously 2 hours and 3 hours. So he traveled for 2 hours at the higher speed an 3 hours at the lower speed.

ANSWER: 2 hours at 6mph; 3 hours at 4mph

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