Deepa rides her bike at an average speed of 30 km/hr and reaches her destination in 6 hours. Hema covers the same distance in 4 hours. If Deepa increases her average speed by 10 km/hr and Hema increases her average speed by 5 km/hr, what would be the difference in their time taken to reach the destination?

### Concept & Time and Speed Variation First establish the constant total distance using the initial conditions. Then, calculate the new speeds and the corresponding new times to find the time difference. $$ \text{Distance} = \text{Speed} \times \text{Time} $$ ### Step-by-Step Solution * **Calculate Distance:** Deepa travels at 30 km/hr for 6 hours. Distance = $30 \times 6 = 180$ km. * **Calculate Hema's Initial Speed:** Hema covers 180 km in 4 hours. Speed = $\frac{180}{4} = 45$ km/hr. * **Calculate New Speeds:** Deepa's new speed = $30 + 10 = 40$ km/hr. Hema's new speed = $45 + 5 = 50$ km/hr. * **Calculate New Times:** Deepa's new time = $\frac{180}{40} = 4.5$ hours. Hema's new time = $\frac{180}{50} = 3.6$ hours. * **Find Time Difference:** Difference = $4.5 - 3.6 = 0.9$ hours. Convert to minutes: $0.9 \times 60 = 54$ minutes. ### Exam Strategy & Shortcut Once the distance is found as 180, calculate the new times as fractions: $180/40 = 9/2$ and $180/50 = 18/5$. The difference is $\frac{9}{2} - \frac{18}{5} = \frac{45 - 36}{10} = \frac{9}{10}$ hours. Multiply by 60 to directly get 54 minutes. ### Common Pitfall Converting $0.9$ hours to 90 minutes instead of correctly multiplying by 60 to get 54 minutes. ### Final Answer Therefore, the correct answer is **54 minutes**.