Discussion
A man travelled first \(2\frac{1}{2}\) hours at 48 km/h, the next 3 hours at 54 km/h and next \(4\frac{1}{2}\) hours at \(x\) km/h. If his average speed for the whole journey is 51.6 km/h, then what is the value of \(x\) ?
Answer: B
The value of x is 52. The distances covered are 2.5 x 48 = 120 km, 3 x 54 = 162 km and 4.5 x x km. The total time is 2.5 + 3 + 4.5 = 10 hours, and at an average speed of 51.6 km/h the total distance is 516 km.
\[ 120 + 162 + 4.5x = 516 \]
\[ 4.5x = 234 \Rightarrow x = 52 \]
The options 50, 56 and 62 do not give a total of 516 km, so the second option is the answer. As a check, the total distance of 120 + 162 + 234 = 516 km divided by the 10 hours gives 51.6 km/h, the average speed in the question.
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