A car travels 60km in first hour and 80km in second — find average speed

Question

A car travels 60 km in the first hour and 80 km in the second hour. Find the average speed of the car over the two hours.

Solution — Step by Step

Distance in first hour: $d_1 = 60$ km

Distance in second hour: $d_2 = 80$ km

Time for each: $t_1 = 1$ hour, $t_2 = 1$ hour

Total time: $t = 2$ hours

d_{total} = d_1 + d_2 = 60 + 80 = 140 \text{ km}

\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{140}{2} = \mathbf{70 \text{ km/h}}

Why This Works

Average speed is always defined as total distance divided by total time. It represents the constant speed that would cover the same total distance in the same total time.

Notice that in this problem, since both time intervals are equal (1 hour each), the average speed happens to equal the simple average of the two speeds: $\frac{60 + 80}{2} = 70$ km/h. This is a coincidence because the times are equal.

Alternative Method — When Times Are NOT Equal

If the problem said the car traveled 60 km at 60 km/h and then 80 km at 80 km/h, the times would differ:

$t_1 = \frac{60}{60} = 1$ hour, $t_2 = \frac{80}{80} = 1$ hour.

Still 70 km/h in this case. But if the problem gave different speeds for different durations (not distances), we must use the full formula.

Common Mistake

Students confuse “average speed” with “average of speeds.” These are equal ONLY when the time intervals are equal. If the car spends equal DISTANCES (not time) at each speed, the average speed is the harmonic mean, not the arithmetic mean. For example, driving 60 km at 60 km/h and 60 km at 120 km/h: average speed = $\frac{120}{1 + 0.5} = 80$ km/h, NOT $\frac{60+120}{2} = 90$ km/h. In our problem, the time intervals are equal, so the arithmetic average correctly gives 70 km/h.

Question

Solution — Step by Step

Why This Works

Alternative Method — When Times Are NOT Equal

Common Mistake

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