Speed and time problem

Question

Sally walks at a speed of 65 m/min, while her sister walks at 75 m/ min. If they are 1680 m apart, how long will they take to meet if they walk toward each other?

 

please provide some working out answer, thank you in advance ...

Answer 1

We need to make use of the formula distance = rate x time. The rate is the speed at which each girl walks. We don't know the total distance that each girl walked. Let's say that Sally walked x miles. Then her sister walked (1680 - x) miles since they started out 1680 m apart. We know that Sally walks at a rate of 65 m/min., and her sister's walking rate is 75 m/min. The time it takes for them to meet is what we are trying to determine. It is also unknown, and we can represent it with the variable t.

 

If distance = rate x time (or d = r x t, using abbreviations), then we can solve for t.

 

t = d/r

 

We have expressed the distance traveled by each girl in terms of x. We are given each girl's rate of walking. All we need to do now is substitute into the above equation and solve for x.

 

x/65 = (1680 - x)/75

 

The figure on the left is the time it takes Sally to reach the meeting point. The figure on the right is the time that it takes her sister to reach the same point. By cross-multiplication, we should now be able to solve for x.

 

75x = 109,200 - 65x

 

140x = 109,200

 

x = 780

 

However, we are not finished with the problem. We expressed the distance walked by each girl in terms of x, but we want to know for what time t do the two girls meet. Remember that d = r x t. Let's solve for t by using Sally's distance, which is x = 780, and her rate, which is 65 m/min.

 

780 = 65t

 

t = 780/65 = 12

 

Therefore, the two girls will meet after 12 min. You could plug in x = 780 into Sally's sister's distance, and you should also receive t = 12.