Question

Let a be the sum of the last four digits and let b be the last digit of your 8-digit student id. (example: for 20245347, a = 19 and b = 7) on a road trip, a driver achieved an average speed of (48.0+a) km/h for the first 54.0 km and an average speed of (43.0-b) km/h for the remaining 86.0 km. what was her average speed (in km/h) for the entire trip? round your final answer to three significant figures

Answer 1

Using the student id given above, a = 19 and b = 7

Average speed for the first 54 km = 48+a km/h

Plug a = 19

Average speed for the first 54 km = 48+19 = 67 km/h

Average speed for remaining 86 km = 43-b km/h where b = 7

Average speed = 36 km/h

Average speed of entire journey = total distance / total time taken

$speed = \frac{distance}{time} and time = \frac{distance}{speed}$

Time taken to cover 54 km = $\frac{54}{67}$ hr

Time take to cover 86 km = $\frac{86}{36}$ hr

Total time taken = 3.2 hours.

Total distance = 86+54= 140 km

Average speed of the entire trip = $\frac{140}{3.2}$ = 43.75 km/ h