Current speed from mixed time units: A boat covers 1 km downstream in 7.5 minutes and travels upstream at 5 km/h. What is the speed of the current?

Introduction / Context:
Converting times consistently to hours avoids unit traps. Once downstream and upstream speeds are known, we can recover still-water and current speeds using the average and half-difference identities.

Given Data / Assumptions:

• Downstream: 1 km in 7.5 min = 1 km / 0.125 h = 8 km/h.
• Upstream speed: 5 km/h.
• Let u be still-water speed, v current speed.

Concept / Approach:
u = (down + up)/2; v = (down − up)/2. These come from u + v and u − v.

Step-by-Step Solution:
Down = 8, Up = 5.u = (8 + 5) / 2 = 6.5 km/h.v = (8 − 5) / 2 = 1.5 km/h.

Verification / Alternative check:
Check: u + v = 6.5 + 1.5 = 8 (downstream), u − v = 6.5 − 1.5 = 5 (upstream). All consistent.

Why Other Options Are Wrong:
1.2, 1.3, 1.6 do not equal the half-difference; 1.1 is arbitrary and inconsistent.

Common Pitfalls:
Treating 7.5 min as 0.75 h; mixing up downstream with upstream; arithmetic slips when halving differences.

Final Answer:
1.5 km/hr