12. Speed, DIstance, Time

Question 1

LEVEL 4

Wayde van Niekerk set the world record for the 400 m with a time of 43 seconds.

Determine his average speed over the course of the race.

Select the correct answer from the list below:

A: 10.5 m/s

B: 8.67 m/s

C: 8.2 m/s

D: 9.3 m/s

CORRECT ANSWER:   D: 9.3 m/s

WORKED SOLUTION:

Because we are looking for speed, we need to cover the s in our speed/distance/time triangle. This tells us we need to divide the distance by the time.

\text{speed}=\dfrac{\text{distance}}{\text{time}}=\dfrac{400}{43}=9.3 m/s (3sf)

Question 2

LEVEL 4

A plane flies between two airports that are 7130 km apart.

Given that the plane travels at a constant speed of 920 km, determines the time the journey took in hours and minutes.

Select the correct answer from the list below:

A: 4 hours and 55 minutes

B: 7 hours and 45 minutes

C: 8 hours and 35 minutes

D: 7 hours and 20 minutes

CORRECT ANSWER: B: 7 hours and 45 minutes

WORKED SOLUTION:

Because we are looking for time, we need to cover the t in our speed/distance/time triangle. This tells us we need to divide the distance by the speed.

\text{time }=\dfrac{\text{distance}}{\text{speed}}=\dfrac{7130}{920}=7.75 hours

So, we have 7 hours and 0.75 hours. This is the same as 7 hours and \dfrac{3}{4} hours, or 7 hours and 45 minutes.

\text{Time in Hours }=\dfrac{20}{60}=\dfrac{1}{3}

Now we can multiply our speed and time.

\text{distance}=\text{speed}\times\text{time} =144\times\dfrac{1}{3}=48 km

So, we have that our total distance covered over these 30 laps is 48 km. But, we only want 1, so we need to divide by 30.
48\div30=1.6 km

Question 3

LEVEL 4

Jenny is a race car driver, driving around a track.

She does 30 laps in 20 minutes, with an average speed of 144 km/h.

Determine the distance travelled in one lap.

Select the correct answer from the list below:

A: 1.6 km

B: 144 km

C: 7.2 km

D: 0.24 km

CORRECT ANSWER:     A: 1.6 km

WORKED SOLUTION:

Because we are looking for distance, we need to cover the d in our speed/distance/time triangle. This tells us we need to multiply speed and time. First of all, our answer needs to be in km, but our speed is in km/h and our time is in minutes. We need to turn these minutes into hours so they will cancel with the hours in km/h.

Now we can multiply our speed and time.

\text{distance}=\text{speed}\times\text{time} =144\times\dfrac{1}{3}=48 km
So, we have that our total distance covered over these 30 laps is 48 km. But, we only want 1, so we need to divide by 30.

48\div30=1.6 km

Question 4

LEVEL 4

Daniel cycles to university 5 days a week.
Daniel takes the same route every day and his journey to university takes 45 minutes at an average speed of 16 mph.
Given that he returns via the same route, determine how many miles he cycles in one week between home and university.

Select the correct answer from the list below:

A: 60 miles

B: 12 miles

C: 120 miles

D: 72 miles

CORRECT ANSWER:  C: 120 miles

WORKED SOLUTION:

Because we are looking for distance, we need to cover the d in our speed/distance/time triangle. This tells us we need to multiply speed and time. First of all, our answer needs to be in miles, but our speed is in mph and our time is in minutes. We need to turn these minutes into hours so they will cancel with the hours in mph.

Now we can multiply our speed and time.

\text{distance}=\text{speed}\times\text{time} =16\times\dfrac{3}{4}=12 miles

So, we have that the distance going one way is 12 miles. However, Daniel will do this 10 times in one week (twice a day, five days a week, 5\times2=10). So, we need to multiply this distance by 10,

12\times10=120 miles

Question 5

LEVEL 4

An unladen swallow travels 1243 m in 113 seconds.

Determine the average speed of the unladen swallow.

Select the correct answer from the list below:

A: 11 m/s

B: 140459 m/s

C: 13.3 m/s

D: 8.9 m/s

CORRECT ANSWER:  A: 11 m/s

WORKED SOLUTION:

Because we are looking for speed, we need to cover the s in our speed/distance/time triangle. This tells us we need to divide the distance by the time.

\text{speed}=\dfrac{\text{distance}}{\text{time}}=\dfrac{1243}{113}=11 m/s

Question 6

LEVEL 4

Calculate the time I took to walk 5 miles if I was going at 2.5 mph.

Select the correct answer from the list below:

A: 1.5 hours

B: 2 hours

C: 2.5 hours

D: 5 hours

CORRECT ANSWER: B: 2 hours

WORKED SOLUTION:

Use the formula \text{Time} = \dfrac{\text{Distance}}{\text{Speed}} and substitute the numbers in:

\text{Time} =\dfrac{(5)}{(2.5)}=\dfrac{5}{(5/2)}=\dfrac{10}{5}=2 hours

Question 7

LEVEL 4

Calculate the distance travelled by a family of 5 who have driven for 5 hours at a speed of 34 mph.

Select the correct answer from the list below:

A: 134 miles

B: 155 miles

C: 160 miles

D: 170 miles

CORRECT ANSWER:D: 170 miles

WORKED SOLUTION:

Use the formula \text{Distance} = \text{Speed} \times \text{Time} and substitute the values into the formula:

34\times 5=170 miles.

Question 8

LEVEL 4

An Amazon driver has been requested to deliver goods to a mansion some 30 miles away from the depot.

It takes the Amazon driver 30 minutes to deliver the goods.

Calculate the average speed of the delivery drive for this journey.

Select the correct answer from the list below:

A: 50 mph

B: 65 mph

C: 54 mph

D: 60 mph

CORRECT ANSWER:   D: 60 mph

WORKED SOLUTION: