Question

do these word problems. show your working clearly in the space provided.

1. the distance round a field is 540 m. ruth runs round the field for 8 times in half an hour. what is her average speed? express your answer in m/min.

1. the distance from singapore to kuala lumpur is 396 km. sam drives from singapore to kuala lumpur at an average speed of 120 km/h. if he starts his journey at 10 45, at what time will he reach kuala lumpur? express the time using the 24-hour clock.

1. mr baker drives from his house to the office at a speed of 82 km/h in 15 minutes. mr taylor, whose house is as far from the office as mr baker, drives for 10 minutes to reach the same office. what is the difference in their driving speed?

Explanation:

Calculate total distance and time for Question 32

We find the total distance run by multiplying the field's perimeter by the number of laps:

$$ \text{Total Distance} = 540\text{ m} \times 8 = 4320\text{ m} $$

The time taken is half an hour, which we convert to minutes:

$$ \text{Total Time} = 30\text{ min} $$

Calculate average speed for Question 32

We divide the total distance by the total time to find the speed in \(\text{m/min}\):

$$ \text{Average Speed} = \frac{4320\text{ m}}{30\text{ min}} = 144\text{ m/min} $$

Calculate travel duration for Question 33

We find the time taken by dividing the distance by the average speed:

$$ \text{Duration} = \frac{396\text{ km}}{120\text{ km/h}} = 3.3\text{ hours} $$

Convert the decimal hours into hours and minutes:

$$ 3.3\text{ hours} = 3\text{ hours} + (0.3 \times 60)\text{ minutes} = 3\text{ hours } 18\text{ minutes} $$

Calculate arrival time for Question 33

We add the travel duration to the start time of 10:45:

$$ 10:45 + 3\text{ hours } 18\text{ minutes} = 13:63 ightarrow 14:03 $$

Expressed in 24-hour format, the arrival time is 14:03.

Calculate distance and speed difference for Question 34

First, find the distance from Mr. Baker's house to the office:

$$ \text{Distance} = 82\text{ km/h} \times \frac{15}{60}\text{ h} = 20.5\text{ km} $$

Next, calculate Mr. Taylor's driving speed to cover this distance in 10 minutes:

$$ \text{Mr. Taylor's Speed} = \frac{20.5\text{ km}}{\frac{10}{60}\text{ h}} = 20.5 \times 6 = 123\text{ km/h} $$

Finally, find the difference in their driving speeds:

$$ \text{Difference} = 123\text{ km/h} - 82\text{ km/h} = 41\text{ km/h} $$

Answer:

Question 32

\(144\text{ m/min}\)

Question 33

14:03

Question 34

\(41\text{ km/h}\)