A cyclist moved at a speed of Xkm/h for 2 hours. He then increased his speed by 2 km/h for the next 3 hours…

Analyze the question

A cyclist rides at X km/h for 2 hours, then at (X + 2) km/h for 3 hours. The total distance is 36 km. We need X, the initial speed.

Concept

Distance = Speed × Time. Add the distances for the two stages and set the total equal to 36 km.

Solution

Stage 1: distance = 2 × X = 2X

Stage 2: the speed is X + 2, so distance = 3(X + 2) = 3X + 6

Total distance:

2X + 3X + 6 = 36 5X + 6 = 36 5X = 30 X = 6

Check:

• Stage 1: 6 × 2 = 12 km
• Stage 2: (6 + 2) × 3 = 24 km
• Total: 12 + 24 = 36 km ✓

The initial speed is 6 km/h, which is option D.

Tip: In "speed × time" word problems, write each stage's distance as its own expression, then add them and set the sum equal to the total. Always plug your answer back in to confirm it. It takes a few seconds and guards against mistakes in the exam hall.