Let’s Solve the Exercise on Average Rates

Let’s Solve the Exercise on Average Rates

Published on ginnyent.net on 14th march, 2019

Photo: http://www.kiplinger.com
The first question says:

  1. On a journey, a motorist travels the first 50km in half hour, then the next 34km in 25 min and the last 7km in 5 min. what is the average speed for the whole journey?

Solution

Here, we will take two steps:

First, we will find the total distance covered

Second, we will find the total time taken to cover the distance.

Total distance covered = 50 + 34 + 7

= 91km

Total time taken = 30min(half hour) + 25min + 5min

= 60 minutes( 1 hour)

Average speed for the whole journey = Total distance covered

Total time taken

= 91km/60

= 1.51km/min

Or 91km/hr.

2. A factory employs 50 workers. 40 earn $90/hour and 10 earn $120 /hour. What is the average hourly rate of pay?

    Solution

    Here, we have to calculate the total pay for the 40 workers in one hour and the total pay for the remaining 10 workers in one hour too.

    Then we will divide the pay per hour by the total number of workers.

    Hourly pay for the 40 workers = $90 x 40

    = $3600

    Hourly pay for the 10 workers = $120 x 10

    = $ 1200

    Total hourly pay = $3600 + $1200

    = $4800

    Hourly pay for the 50 workers = $4800/50

    = $96/hr

    3. A lorry travelled 84km between two towns. The first 60km of road was un- tarred and the average speed over this part was 30km/hr. If the average speed for the whole journey was 36km/hr, calculate the average speed over the good part of the road.
    Solution

    Here, we will find the distance of the tarred and un-tarred part of the road.

    From the question, the un-tarred part of the road was 60km and the total distance between the two towns is 84km.

    Therefore the tarred part of the road = 84km – 60km

    = 24km

    Also from the question, the average speed for the whole journey was 36km/hr and we were given the average speed for the un-tarred part of the road as 30km/hr.

    Now we would find the time it took to cover each parts of the roads.

    For the un-tarred part, time taken = distance/speed

    = 60km

    30km

    = 2 hours

    Now, we have to apply our knowledge of getting the average rate to find the time taken to cover the tarred part of the road

    Average speed for the journey

    = total distance covered

    total time taken

    But average speed for the whole journey = 36km/hr

    Since we don’t know the time it took to cover the tarred part of the road, let’s call it ‘x’.

    Therefore, 36 = 84

    2 + x

    If you cross multiply, you’d have 36 (2 + x) = 84

    Opening the bracket, we have 72 + 36x = 84km

    Make x the subject of formuar, we have : 84 -72

    36

    = 0. 33hr

    The average speed it took to cover the tarred part of the road = 24km/0.33hr

    = 72km/hr

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