Question

Two cars start from the same point simultaneously and in the same direction. The first car travels at $40$ km/h, and the speed of the second car is $125$ per cent of the speed of the first car. Thirty minutes later a third car starts from the same point and in the same direction. It overtakes the second car $1.5$ h later than it overtook the first car. What is the speed of the third car?

Answer 1

Speed of Second car is $⟹\frac{125}{100}\times 40=50$

Let velocity of Third car be $x$

Let $t$ be Time taken to overtake first car

Distance covered is $xt=40t+20$

$⟹x=\frac{40t+20}{t}$

Distance covered to overtake second car is $x(t+1.5)=50(t+1.5)+25$

$⟹\frac{40t+20}{t}(t+1.5)=50t+100$

$⟹t^2+2t-3=0$

$⟹t=1,-3$

Time cannot be negative So $t=1⟹x=60$