Question

some cars were timed on a 100km journey. Their average time was 1hr28min14s.
(a). Round this time to the nearest 1/4 hour.
(b). Use the rounded time to find the approximate average speed for the journey in km/h. Give your answer to 1 s.f

Answer 1

To solve the problem, we'll follow the two parts step by step.

### (a) Rounding the Time to the Nearest 1/4 Hour

The average time given is 1 hour, 28 minutes, and 14 seconds.

1. First, we convert the time to hours:
- 1 hour is 1 hour.
- 28 minutes is \( \frac{28}{60} \) hours = 0.4667 hours (approx).
- 14 seconds is \( \frac{14}{3600} \) hours = 0.00389 hours (approx).

Adding these together:
\[
1 + 0.4667 + 0.00389 \approx 1.4706 \text{ hours}
\]

2. Next, we round this time to the nearest 1/4 hour (which is 0.25 hours).
- The quarter-hour marks are: 0.00, 0.25, 0.50, 0.75, 1.00, 1.25, 1.50, etc.
- 1.4706 falls between 1.25 and 1.50.

To decide which quarter it is closer to, we find the midpoint:
\[
\frac{1.25 + 1.50}{2} = 1.375
\]
Since 1.4706 is greater than 1.375, it rounds up to 1.50 hours.

### Answer (a):
The rounded time is **1.50 hours**.

### (b) Calculating Approximate Average Speed

To find the average speed, we use the formula:
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\]

Here, the distance is 100 km, and the time is 1.50 hours.

Calculating the speed:
\[
\text{Speed} = \frac{100 \text{ km}}{1.50 \text{ hours}} \approx 66.67 \text{ km/h}
\]

Rounding this to 1 significant figure:
- The first significant figure is 6, so we round 66.67 to \( 70 \) km/h (rounding up).

### Answer (b):
The approximate average speed for the journey is **70 km/h** (to 1 significant figure).