Question

In a 100 m race, A runs at 8 km per hour. A gives B a start of 4 m and still beats him by 15 seconds, what is the speed of B?

• A. 2.40 km/hr
• B. 6.76 km/hr
• C. 3.76 km/hr
• D. 5.76 km/hr

Hint:

Ensure consistent units throughout the calculation. Convert km/hr to m/s or vice versa as needed. Remember that if A beats B by a certain time, B takes that much longer to cover his distance.

Answer 1

The Correct Option is D

Step 1: Convert the speed of A to m/s.
Speed of A = 8 km/hr = \( 8 \times \frac{1000}{3600} \) m/s = \( \frac{80}{36} \) m/s = \( \frac{20}{9} \) m/s Step 2: Calculate the time taken by A to finish the race.
Time taken by A = \( \frac{\text{Distance}}{\text{Speed}} = \frac{100}{\frac{20}{9}} = 100 \times \frac{9}{20} = 5 \times 9 = 45 \) seconds. Step 3: Determine the distance covered by B and the time taken by B.
B gets a start of 4 m, so B runs \( 100 - 4 = 96 \) m.
A beats B by 15 seconds, so B takes \( 45 + 15 = 60 \) seconds to cover 96 m.
Step 4: Calculate the speed of B in m/s.
Speed of B = \( \frac{\text{Distance}}{\text{Time}} = \frac{96}{60} \) m/s = \( \frac{8}{5} \) m/s = 1.6 m/s Step 5: Convert the speed of B to km/hr.
Speed of B = \( 1.6 \times \frac{3600}{1000} \) km/hr = \( 1.6 \times 3.6 \) km/hr = 5.76 km/hr