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Will and Grace are canoeing on a lake.  Will rows at 50 meters per minute and Grace rows at 20 meters per minute. Will starts rowing at 2 p.m. from the west end of the lake, and Grace starts rowing from the east end of the lake at 2 p.m. If they always row directly towards each other, and the lake is 3800 meters across from the west side of the lake to the east side, at what time will the two meet?

Jul 11, 2023

#1
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Together, every minute they are getting 70 meters a minute closer to each other. See if you can get the answer from that!

Jul 11, 2023
#2
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Since they are rowing toward each other we can combine their speeds together, therefore :

20 meters per minute + 50 meters per minute = 70 meters per minute

In this problem, we can use the equation Distance = Speed x Time

Distance:  3800 meters

Speed: 70 meters per minute

Time : x

3800 meters = 70 meters per min ⋅ x

3800 meters / 70 meters per minute = x

54.285...  minutes = x

These numbers are definitely not ideal for this problem however I would use 54.5 minutes or 55 minutes as the total time to reach each other

Now since they both started at 2 pm we can simply add the time to 2 pm:

2:00 pm + 54.5 minutes = 2: 54: 30 pm

Or

2 : 00 pm + 55 minutes = 2:55 pm

Jul 11, 2023
#3
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Very good.  I'll just add that 0.285 minute is 17 seconds.

If you're going to call it 2:54:30 you might as well call it 2:54:17

and be precise, since this is just a math problem and theoretical.

.

Bosco  Jul 11, 2023