A tractor moves at a uniform speed of $60\text{ km/h}$. A maintenance pickup truck starts from the same origin $1\text{ hour}$ later (giving the tractor a $50\text{ km}$ initial lead) and travels along the same straight road at $90\text{ km/h}$. The time taken by the pickup truck to overtake the tractor is ________ $\text{hours}$ (round off to two decimal places).
Answer Key:
1.67
Step-by-Step Solution & Explanation
The relative speed between the two vehicles moving in the same direction is:
$v_{rel} = v_2 - v_1 = 90 - 60 = 30\text{ km/h}$
Time to close the initial distance gap $d = 50\text{ km}$:
$t = \frac{d}{v_{rel}} = \frac{50}{30} = 1.67\text{ hours}$