Average speed with two different speeds — ratio of distances: A man travels part of a journey at 20 km/h and the rest at 70 km/h. His overall average speed is 50 km/h. What is the ratio of the distance covered at 20 km/h to that covered at 70 km/h?

Introduction / Context:When average speed over a whole trip is known and the trip has only two constant-speed segments, ratios can be derived without the absolute distance.

Given Data / Assumptions:

• Speeds: v1 = 20 km/h, v2 = 70 km/h
• Average over the entire journey: V_avg = 50 km/h
• Let distances be d1 and d2 for the two legs.

Concept / Approach:Average speed V_avg = (d1 + d2) / (d1/20 + d2/70). Let x = d1/d2 and solve for x.

Step-by-Step Solution:

Verification / Alternative check:Try d1 : d2 = 4 : 21 with any scaling; average recomputes to 50 km/h.

Why Other Options Are Wrong:Other ratios fail to satisfy the average speed relationship.

Common Pitfalls:Using time ratios instead of distance ratios in the average speed formula.

Final Answer:4 : 21