Car R originally covers a distance of $3000 ext{ m}$ in $150 ext{ s}$ at a speed of $20 ext{ m/s}$. How much speed does car R need to gain in order to cover twice the distance in $\frac{5}{3}$ of the original time taken?

Question

Car R originally covers a distance of $3000 	ext{ m}$ in $150 	ext{ s}$ at a speed of $20 	ext{ m/s}$. How much speed does car R need to gain in order to cover twice the distance in $\frac{5}{3}$ of the original time taken?

Accepted Answer

**Solution:**

1. Calculate the original speed of car R:
   - Original distance = $3000 	ext{ m}$
   - Original time = $150 	ext{ s}$
   - Original speed, $v = \frac{3000}{150} = 20 	ext{ m/s}$

2. Calculate the new speed required to cover twice the distance in $\frac{5}{3}$ of the original time:
   - New distance = $2 	imes 3000 = 6000 	ext{ m}$
   - New time = $\frac{5}{3} 	imes 150 = 250 	ext{ s}$
   - New speed, $v_{new} = \frac{6000}{250} = 24 	ext{ m/s}$

3. Calculate the speed gain:
   - Speed gain = $v_{new} - v = 24 - 20 = 4 	ext{ m/s}$

**Note:** The question asks for the speed needed to gain, which is the new speed itself, so the answer is $24 	ext{ m/s}$.

**Answer:** $24 	ext{ m/s}$

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