Question : Sarthak completed a marathon in 4 hours and 35 minutes. The marathon consisted of a 10 km run followed by a 20 km cycle ride and the remaining distance, again a run. He ran the first stage at 6km/h and then cycled at 16km/h. How much distance did Sarthak cover in total, if his speed in the last run was just half that of his first run?
Option 1: 5 km
Option 2: 35 km
Option 3: 40 km
Option 4: 45 km
Correct Answer: 35 km
Solution :
Let the distance be $x$ km.
Time = 4 hour 35 minutes = 4$\frac{35}{60}$ = 4$\frac{7}{12}$ = $\frac{55}{12}$ hours
Time = $\frac{\text{Distance}}{\text{Speed}}$
According to the question,
$\frac{10}{6}+\frac{20}{16}+\frac{x-30}{3}$ = $\frac{55}{12}$
⇒ $\frac{5}{3}+\frac{5}{4}+\frac{x}{3}-10$ = $\frac{55}{12}$
⇒ $\frac{x}{3}+(\frac{5}{3}+\frac{5}{4}-10)$ = $\frac{55}{12}$
⇒ $\frac{x}{3}+(\frac{20+15-120}{12})$ = $\frac{55}{12}$
⇒ $\frac{x}{3}-\frac{85}{12}$ = $\frac{55}{12}$
⇒ $\frac{x}{3}$ = $\frac{55}{12}+\frac{85}{12}$
⇒ $\frac{x}{3}$ = $\frac{140}{12}$
⇒ $x=35$ km
Hence, the correct answer is 35 km.
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