Question

Jack went for a mountain hike. On his way up, he traveled

at a speed of 2 mph. He reached the summit in 3 hours. On his
way back down, Jack jogged at a speed of 5 mph. Write
the formula that describes how the distance Jack covered during
the hike depends on the amount of time that he traveled.

Answer 1

d = (20/7)t

Explanation:

You want the distance traveled as a function of travel time if Jack's speed going up was 2 mph and going down was 5 mph.

Time

The relation between time, speed, and distance is ...

t = d/s

If the total distance is d, the total travel time up and back is ...

t = t1 +t2

t = (d/2)/(2) +(d/2)/5 = d(1/4 +1/10) = 0.35d

Solving for distance, we have ...

d = t/0.35

d = (20/7)t . . . . miles, where t is in hours

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