Alice is faster than Bob, Alice and Bom each walk 30 km. The sum of their speeds is 8 km/hr and sum of time taken by them is 16 hours. Then Alice’s speed is equal to
Answer & explanation
Correct answer: option 1
Let Alice speed = x km/h
Bob’s speed = 8 – x km/h
According to question
$\frac{30}{x}+\frac{30}{(8-x)}=16$
$30(8 – x) + 30x = 16x(8 – x)$
$240 – 30x + 30x = 128x – 16x^2$
$16x^2 – 128x + 240 = 0$
$x^2 – 8x + 15 = 0$
$(x – 5) (x – 3)$
$x = 3$ and $x = 5$