Shantanu rides a motorcycle for 715 km at constant speed v. If he had ridden 10 km/h faster, he would have saved 2 hours over the same distance. What is his original speed v (in km/h)?

Introduction / Context:This is a classic “time saved with higher speed” equation. Over a fixed distance, increasing speed reduces time according to t = D/v. Setting up the difference in times equal to the saved amount yields a quadratic in v that can be solved exactly.

Given Data / Assumptions:

• Distance D = 715 km.
• Original speed v km/h; faster speed v + 10 km/h.
• Time saved = 2 h.

Concept / Approach:Equation: 715/v − 715/(v+10) = 2. Simplify to solve for v. Positive, realistic highway values are expected.

Step-by-Step Solution:

Verification / Alternative check:Times: at 55 km/h → 13 h; at 65 km/h → 11 h; saving = 2 h as required.

Why Other Options Are Wrong:60 or 65 km/h do not yield a 2-hour difference for 715 km; 36 km/h is too low and unrealistic here.

Common Pitfalls:Arithmetic slips in clearing denominators; accepting the negative quadratic root.

Final Answer:55 km/h