Question

A car moves a distance of 200 m. It covers the first half of the distance at speed 40 km/h and the second half of distance at speed v. The average speed is 48 km/h. The value of v is

• A. 56 km/h
• B. 60 km/h
• C. 50 km/h
• D. 48 km/h

Answer 1

The Correct Option is B

To find the value of \( v \), we need to analyze the given problem using the concept of average speed and the formula for time and distance.

1. First, calculate the time taken to cover each half of the distance. The total distance is 200 m, so each half is \( 100 \, \text{m} \).
2. The speed for the first half is 40 km/h. Convert this speed into meters per second:

40 \, \text{km/h} = \frac{40 \times 1000}{3600} \, \text{m/s} = \frac{40000}{3600} \, \text{m/s}

3. Now, calculate the time taken to cover the first half (100 m) of the distance:

t_1 = \frac{100}{\frac{40000}{3600}} = \frac{100 \times 3600}{40000} \, \text{s}

t_1 = \frac{9}{10} \, \text{s}

4. Next, let's solve for the time taken for the second half with speed \( v \). Assume the speed \( v \) is in km/h:

t_2 = \frac{100}{\frac{v \times 1000}{3600}} = \frac{100 \times 3600}{v \times 1000} \, \text{s} = \frac{360}{v} \, \text{s}

5. The average speed formula is given by:

v_{\text{avg}} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{200}{t_1 + t_2}

6. Substitute the average speed (48 km/h converted to m/s):

48 \, \text{km/h} = \frac{48 \times 1000}{3600} \, \text{m/s} = \frac{48000}{3600} \, \text{m/s} = \frac{40}{3} \, \text{m/s}

7. Set up the equation using the average speed:

\frac{40}{3} = \frac{200}{t_1 + t_2} = \frac{200}{\frac{9}{10} + \frac{360}{v}}

8. Substitute \( t_1 \) and solve for \( v \):

Simplifying further, we have:

t_1 + t_2 = \frac{9}{10} + \frac{360}{v}

Substitute into the average speed equation:

\frac{40}{3} = \frac{200}{\frac{9}{10} + \frac{360}{v}}

Cross-multiply and solve for \( v \):

40v = 600(90v - 3600 + 360v)

40v = 60(9v + 3600)

180v = 216000

Solve for \( v \):

v = 60 \, \text{km/h}

Thus, the correct value of \( v \) is 60 km/h.