Question

2.1.5 there are two alternative routes from piet retief to nelspruit.

• route a is 257 km long with a driving time of 2 hours 57 minutes.
• route b is 263 km long with a driving time of 2 hours 53 minutes.

calculate the difference in the distance and driving time between the two routes.
2.1.6 mr mnisi uses route a to depart from pietretief at 17:30 and travels to nelspruit at an average speed of 90 km/h. he calls his wife to inform her that he will arrive home at 20:15.
verify, with calculations, whether his timing is correct.
you may use the formula :
speed = \frac{distance}{time}

Explanation:

Step1: Calculate distance difference

Subtract the length of Route A from Route B.
$263 - 257=6$ km

Step2: Calculate time difference

First convert times to minutes. Route A: 2 hours 57 minutes = $2\times60 + 57=120 + 57 = 177$ minutes. Route B: 2 hours 53 minutes = $2\times60+53 = 120 + 53=173$ minutes. Then subtract.
$177-173 = 4$ minutes

Step3: Calculate expected time for Route A in 2.1.6

Use the formula $Time=\frac{Distance}{Speed}$. Distance of Route A is 257 km and speed is 90 km/h.
$Time=\frac{257}{90}\approx2.86$ hours. Convert 0.86 hours to minutes: $0.86\times60\approx52$ minutes. So the total time is about 2 hours 52 minutes.

Step4: Calculate arrival time

Departure time is 17:30. Add 2 hours 52 minutes. 17:30 + 2 hours = 19:30, 19:30+52 minutes = 20:22.

Answer:

Distance difference: 6 km
Time difference: 4 minutes
Mr Mnisi's timing is incorrect as he should arrive at 20:22 not 20:15.