SOLUTION: A man travels from A to B at 4 km/h and from B to A at 6 km/h. The total journey takes 45 minutes. Find the distance travelled.

Question 1209176: A man travels from A to B at 4 km/h and from B to A at 6 km/h. The total journey takes 45 minutes. Find the distance travelled.
Found 3 solutions by math_tutor2020, greenestamps, josgarithmetic:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Answer: 3.6 km

Work Shown

distance = rate*time
d = r*t

Going from A to B
d = r*t
d = 4*t
t = d/4

It takes d/4 hours to travel from A to B at a speed of 4 km/hr, where d is the distance from A to B.

Similar steps will show that it takes d/6 hours to travel from B to A at a speed of 6 km/hr.
This assumes the person took the same route to go back to A, or they took a route of equal length.

The two time values must add to 45 minutes = 45/60 = 3/4 of an hour.
Use the hour value because d/6 and d/4 are in hours.

(d/4) + (d/6) = 3/4
12*( (d/4) + (d/6) ) = 12*(3/4)
12*(d/4) + 12*(d/6) = 12*(3/4)
3d + 2d = 9
5d = 9
d = 9/5
d = 1.8 km exactly. This value hasn't been rounded.
This is the one-way distance.
The round trip distance is double that and it is 2*1.8 = 3.6 km

Another way to solve
(d/4) + (d/6) = 3/4
(3d/12) + (2d/12) = 3/4
(3d+2d)/12 = 3/4
5d/12 = 3/4
5d*4 = 12*3
20d = 36
d = 36/20
d = (9*4)/(5*4)
d = 9/5
d = 1.8 is the one-way distance; which doubles to a round trip distance of 3.6 km

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Another approach is to convert each km per hr speed value into km per min.
To do so, divide by 60.
4 km per hr = 4/60 = 1/15 of a km per min
6 km per hr = 6/60 = 1/10 of a km per min

Using d = r*t, we get this equation when going from A to B
d = (1/15)*t
which can be rearranged to
t = 15d
This is the time it takes, in minutes, to travel from A to B.

Similar steps will show it takes 10d minutes to travel from B to A.

Total travel time = 15d+10d = 25d = 45 min
25d = 45
d = 45/25
d = (9*5)/(5*5)
d = 9/5
d = 1.8 km is the one-way distance which doubles to 3.6 km and it's the final answer.

Edit: tutor greenestamps makes a great point. I had a brainfart for some reason. My error has been fixed (changed the answer from 1.8 km to 3.6 km)

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

The response from the other tutor shows a few methods for solving the problem which are all variations of the standard algebraic method.

Here is a non-standard and very different method which I personally prefer for solving this particular kind of problem.

The distances both directions are the same; the ratio of the speeds in the two directions is 4:6 = 2:3. That means that the ratio of times at the two speeds is 3:2.

The ratio of the time spent at 4 km/h to the time spent at 6 km/h is 3:2, and the total time is 45 minutes. Use mental arithmetic or any formal process you want to find that he spent 27 minutes at 4 km/h and 18 minutes at 6 km/h.

The number of kilometers traveled at 4 km/h for 27 minutes or 9/20 hours is 4*9/20 = 36/20 = 1.8.

So the distance traveled from A to B and back is 2*1.8 = 3.6 km.

ANSWER: 3.6 km (total distance traveled)

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For tutor @math_tutor2020....

Your calculations all show that 1.8km is the ONE WAY distance, not the total distance traveled....

Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!

SPEED TIME DISTANCE A to B 4 d/4 d B to A 6 d/6 d TOTAL 0.75

Question asks for the TOTAL, or 2d.

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