Question

A man decides to travel 80 km in 8 hours partly by foot and partly on a bicycle. If his speed on foot is 8 km/hour and on bicycle is 16 km/hour, what distance would he travel on foot?

• A. 20 km
• B. 30 km
• C. 48 km
• D. 60 km

Hint:

Set variables for unknown distances, write total time as sum of times for each part, and solve the equation.

Answer 1

The Correct Option is C

Let the distance travelled on foot be \(x\) km.
Then the distance travelled on bicycle \(= 80 - x\) km.
Given:
Speed on foot \(= 8\) km/hr
Speed on bicycle \(= 16\) km/hr
Total time taken \(= 8\) hours
Time taken to travel \(x\) km on foot \(= \frac{x}{8}\) hours.
Time taken to travel \(80 - x\) km on bicycle \(= \frac{80 - x}{16}\) hours.
Total time is sum of both times:
\[ \frac{x}{8} + \frac{80 - x}{16} = 8 \] Multiply through by 16 to clear denominators:
\[ 2x + (80 - x) = 128 \] \[ 2x + 80 - x = 128 \] \[ x + 80 = 128 \] \[ x = 128 - 80 = 48 \] So, the man travels \(\boxed{48}\) km on foot.
Verification:
Time on foot = \(\frac{48}{8} = 6\) hours.
Time on bicycle = \(\frac{80 - 48}{16} = \frac{32}{16} = 2\) hours.
Total time = \(6 + 2 = 8\) hours (matches given).
Therefore, the answer is correct.