Word problem

Question

Man travels 4.2 miles back and forth to work daily. It takes him 72 min.  He much time would he save in 129 days  if he moves and now travels 1.7 miles daily for the same number of days travelling at the same rate?

Answer 1

Hi Lo, I hope that the following will help you with the question.

Concepts that you need to know:
1) Travelling at the same rate means to travel at the same speed and speed = distance/ time.

2) Since speed = distance/ time, time = distance/speed.

Problem solving idea:
The first two sentences give you information to find the travelling speed, speed = distance/ time. Using time = distance/speed, find the time taken to travel 1.7 miles with the calculated speed. Next, find the time saved daily and multiply by 129 to find the time saved in 129 days.

(With better problem solving skills, you can have shorter solution. Shorter solution is available at the end of the post.)

Solution:
speed = 4.2/72

           = 7/120 miles per min
time taken to travel 1.7 miles = 1.7/(7/120)
                                                  = 204/7 min

time saved daily = 72 - 204/7

                            = 300/7 min

time saved in 129 days = (300/7)(129)

                                       = 5528 4/7 min
In conclusion, the time saved in 129 days is 5528 4/7 min.

 

Checking of solution:
There are other ways to do it with shorter working. For example,

Distance saved in 129 days = (4.2 - 1.7)(129)

                                              = 322.5 miles

Speed = 4.2/72 miles per min

Time saved in 129 days = 322.5/(4.2/72)

                                        = 5528 4/7 min