Problem 1A-1: Average Speed

At time t = 0 a car starts to move from point A along a horizontal line across as shown in the picture. Three more measuring points, B, C and D are set up along the line. The distances of those additional points from point A and the time when the car passes them are tabulated as follows:

```

Measuring points
A
B
C
D

Distance from point A, in kilometers (km)
0.00
0.10
0.50
1.50

Time the car passes, in minutes (min)
0.00
0.50
1.50
3.00

```
What is the average speed of the car between A and B, and between C and D? Express the answers in km/min, km/hour, and mile/hour, using the conversion 1 mile = 1.61 km.

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Solution:

Speed is defined as distance ÷ time.

```The average speed from A to B = (0.10 - 0 km)÷(0.50 - 0 min)
= (0.10 km)÷(0.50 min) = 0.20 km/min
= (0.10 km)÷((0.50 min)÷(60 min/hr)) = (0.1×60÷0.50  km/hr)
= 12.0 km/hr
=  ((12.0 km/hr)÷(1.61 km/mile)) =7.45 mile/hr.

The average speed from C to D = (1.50 - 0.50 km)÷(3.00 - 1.50 min)
= (1.00 km)÷(1.50 min) = 0.67 km/min.
= (1.00 km)÷((1.50 min)÷(60 min/hr))
= (1.00×60÷1.50 km/hr)
= 40.0 km/hr.
= ((40.0 km/hr)÷(1.61 km/mile)) =24.8 mile/hr.
```