Question

A motorist covers a distance of $39$ km in $45$ minutes by moving at a speed of $x$ kmph for the first $15$ minutes, then moving at double the speed for the next $20$ minutes, then again moving at his original speed for the rest of the journey, then $x$ in kmph is equal to:

• A. $31.2$
• B. $36$
• C. $40$
• D. $52$

Answer 1

The correct option is B $36$

Case 1:

Speed is $x$ km/hr

Time is 15 min = $1/4$ hr

$\therefore Distance=\frac{Speed}{Time}=\frac{x}{4}$ km

Case 2:

Speed is $2x$ km/hr

Time is 20 min = $1/3$ hr

$\therefore Distance=\frac{Speed}{Time}$ = $\frac{2x}{3}$ km

Case 3:

Speed is $x$ km/hr

Time is 10 min = $1/6$ hr

$\therefore Distance=\frac{Speed}{Time}=\frac{x}{6}$ km

Total distance is $39$km

$\therefore \frac{x}{4}+\frac{2x}{3}+\frac{x}{6}=39$

Taking LCM as 12 and multiplying 12 on both sides, we get

$\frac{3x+8x+2x}{12}\times 12=39\times 12$

$13x=39\times 12$

$x=\frac{39\times 12}{13}$

$x=36$km/hr.