Question : Sunil drove for 2 hours at a rate of 50 miles per hour and 3 hours at 60 miles per hour. What was his average speed for the whole journey?
Option 1: 55 miles per hour
Option 2: 50 miles per hour
Option 3: 56 miles per hour
Option 4: 52 miles per hour
Correct Answer: 56 miles per hour
Solution :
Let's denote the total distance travelled as $D$ and the total time as $T$.
T
1
= 2 hours and T
2
= 3 hours
Speed
1
= 50 miles per hour and Speed
2
= 60 miles per hour
⇒ Distance covered D
1
= 2 × 50 = 100 miles
⇒ Distance covered D
2
= 3 × 60 = 180 miles
⇒ Total distance = D
1
+ D
2
= 100 + 180 = 280
⇒ Total time = 2 + 3 = 5 hours
⇒ Average speed = $\frac{\text{Total distance}}{\text{Total time}}$ = $\frac{280}{5}$ = 56
Hence, the correct answer is 56 miles per hour.
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