Mathematics 2018 JAMB Past Questions - Question 14: A train moves from P at Q at an average speed of 40km/hr and immediately returns from Q is P. Through the 45km/hr. find the average speed for the entire lourney

Correct Answer

D

Explanation

Average speed = p to Q = 90km/hr = 90 45/2 = 135 / 2 = 7km /hr.To find the average speed for the entire journey, we can use the formula for average speed, which is the total distance traveled divided by the total time taken.Let's denote the distance from P to Q as D. Since the train travels from P to Q at 40 km/hr and then returns from Q to P at 45 km/hr, the total distance traveled is 2D (to account for the return journey).The time taken to travel from P to Q at 40 km/hr is D/40, and the time taken to return from Q to P at 45 km/hr is also D/45.The total time taken for the entire journey is:\[ \frac{D}{40} + \frac{D}{45} \]The average speed for the entire journey is:\[ \frac{2D}{\frac{D}{40} + \frac{D}{45}} \]Simplifying the expression:\[ \frac{2D}{\frac{9D + 8D}{360}} \]\[ \frac{2D}{\frac{17D}{360}} \]\[ \frac{2D \times 360}{17D} \]\[ \frac{720D}{17D} \]\[ \frac{720}{17} \]So, the average speed for the entire journey is approximately 42.35 km/hr.