Question

John is faster than Jude. John and Jude each walk $20$ km. The sum of their speeds is $9$ km/hr and the sum of their time taken is $9$ hrs. What is the time taken by John in hours?

• A. $2$ hours
• B. $3$ hours
• C. $4$ hours
• D. $5$ hours

Answer 1

Answer: (C)

$4$ hours

Let $x$ be the speed of John. Then speed of Jude $=9-x$
Time taken by John $=$ $\frac{20}{x}$
Time taken by Jude $=$ $\frac{20}{9-x}$
Time (John) $+$ Time (Jude) $=9$ hours.
$\frac{20}{x}+\frac{20}{9-x}=9$
$20(9-x)+20x=9x(9-x)$
$180=81x-9x^2$
Divide $9$ on both sides, we get
$x^2-9x+20=0$
On factoring, we get
$(x-5)(x-4)=0$
$x=5$ or $4$
Time taken by John $=$ $\frac{20}{x}$
$=$ $\frac{20}{5}$ $=4$ hours.