The speed of a boat in still water and the speed of the current are in the ratio $6 : 1$. The difference between the distance covered by the boat in 2 hours upstream and 2 hours downstream is $8 ext{ km}$. Compare the following quantities:

**Quantity 1:** Speed of the boat in still water

**Quantity 2:** Speed of a cyclist who covers $28 ext{ km}$ in 2 hours

Which of the following is true?

Question

The speed of a boat in still water and the speed of the current are in the ratio $6 : 1$. The difference between the distance covered by the boat in 2 hours upstream and 2 hours downstream is $8 	ext{ km}$. Compare the following quantities:

**Quantity 1:** Speed of the boat in still water

**Quantity 2:** Speed of a cyclist who covers $28 	ext{ km}$ in 2 hours

Which of the following is true?

Accepted Answer

**Solution:**

1. Let the speed of the boat in still water be $6x$ and the speed of the current be $x$ (given ratio $6:1$).

2. The speed downstream = speed of boat + speed of current = $6x + x = 7x$.

3. The speed upstream = speed of boat - speed of current = $6x - x = 5x$.

4. Distance covered downstream in 2 hours = $2 	imes 7x = 14x$.

5. Distance covered upstream in 2 hours = $2 	imes 5x = 10x$.

6. The difference between these distances is given as $8 	ext{ km}$:
   $$14x - 10x = 8 \ 4x = 8 \ x = 2$$

7. Therefore, speed of the boat in still water = $6x = 6 	imes 2 = 12 	ext{ km/h}$.

8. Speed of the cyclist who covers $28 	ext{ km}$ in 2 hours:
   $$rac{28}{2} = 14 	ext{ km/h}$$

9. Comparing the two quantities:
   - Quantity 1 = $12 	ext{ km/h}$
   - Quantity 2 = $14 	ext{ km/h}$

10. Since $12 < 14$, Quantity 1 is less than Quantity 2.

**Answer:** (c) Quantity 1 < Quantity 2

Answer

Answer

Answer

Answer