Speed from time-change over fixed distance A car covers 840 km at uniform speed. If its speed were 10 km/h faster, the trip would take 2 hours less. What was the original speed?

Introduction / Context:
When speed increases by a fixed amount for the same distance, the time decreases in a way that leads to a rational equation. Solving for the original speed yields a quadratic that typically factors neatly in standard test problems.

Given Data / Assumptions:

• Distance D = 840 km.
• Original speed v; new speed v + 10.
• Time saved = 2 h.

Concept / Approach:
Equation: 840/v − 840/(v + 10) = 2. Clear denominators to solve for v and take the positive root.

Step-by-Step Solution:

Verification / Alternative check:
Times: 840/60 = 14 h; 840/70 = 12 h; difference 2 h.

Why Other Options Are Wrong:
45, 50, 75 do not satisfy the time-difference equation.

Common Pitfalls:
Setting up 840/(v + 10) − 840/v = 2 (sign reversed) or canceling incorrectly.

Final Answer:
60 km/h