Ritesh drove at a speed of 60 km/h for 8 hours. For how many hours should he now drive at a speed of 80 km/h for the overall average speed to become 72 km/h?

Options

A. 8
B. 12
C. 10
D. 15

Answer

To solve the problem, we need to find out how many hours Ritesh should drive at a speed of 80 km/h so that his overall average speed becomes 72 km/h after driving for 8 hours at 60 km/h.

Let's break it down step by step:

### Step 1: Calculate the distance traveled at 60 km/h
Ritesh drove for 8 hours at a speed of 60 km/h.

Distance = Speed × Time
Distance = 60 km/h × 8 hours = 480 km

### Step 2: Let the time driven at 80 km/h be 't' hours
Now, we need to find out how long he should drive at 80 km/h. Let’s denote this time as 't'.

### Step 3: Calculate the distance traveled at 80 km/h
Distance = Speed × Time
Distance = 80 km/h × t hours = 80t km

### Step 4: Calculate the total distance
Total distance traveled = Distance at 60 km/h + Distance at 80 km/h
Total distance = 480 km + 80t km = (480 + 80t) km

### Step 5: Calculate the total time
Total time taken = Time at 60 km/h + Time at 80 km/h
Total time = 8 hours + t hours = (8 + t) hours

### Step 6: Set up the equation for average speed
Average speed = Total distance / Total time
We want the average speed to be 72 km/h. Therefore, we can set up the equation:

\[ 72 = \frac{480 + 80t}{8 + t} \]

### Step 7: Cross-multiply to solve for 't'
Cross-multiplying gives us:

\[ 72(8 + t) = 480 + 80t \]

Expanding both sides:

\[ 576 + 72t = 480 + 80t \]

### Step 8: Rearranging the equation
Now, rearranging the equation to isolate 't':

\[ 576 - 480 = 80t - 72t \]

\[ 96 = 8t \]

### Step 9: Solve for 't'
Dividing both sides by 8:

\[ t = \frac{96}{8} = 12 \]

### Conclusion
Ritesh should drive for **12 hours** at a speed of 80 km/h to achieve an overall average speed of 72 km/h.

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