Pilar is playing with a motorized toy boat.
She puts the boat in a lake and it travels $400$ m at a constant speed.
On the way back to Pilar, the boat travels the same route at the same speed for $2$ minutes, and then Pilar uses the remote control to increase the boat's speed by $10$ m/min.
So the return trip is $60$ seconds faster. How long does the return trip take?

Open in App

Solution

The trip normally takes $8$ minutes:
Step-by-step explanation:
The given information states that the away distance the boat traveled : $400$ m
The time traveled at the same initial speed , v₁, by the boat on the way back : $2$ minutes
The increase in speed of the boat by Pilar : $10$ m/min
The new speed, $v_{2} = v_{1} + 10$
The time for the return trip, $t_{2} = 60$ seconds (1 minute) faster than time for the trip, $t_{1}$
$t_{2} = t_{1} - 1$
Therefore we have;
$v_{1} \times t_{1} = v_{1} \times 2 + v_{2} \times (t_{2} - 2) = 400 v_{1} \times 2 + (v_{1} + 10) \times (t_{2} - 2) = 400 (v_{1} + 10) \times t_{2} - 20 = 400 But v ₁ = \frac{400}{t_{1}} = \frac{400}{(t_{2} + 1)}$
Which gives;
$(\frac{400}{(t_{2} + 1)} + 10) \times t_{2} - 20 = 400 10 \times \frac{({t_{2}}^{2} + 36 \cdot t_{2} - 2)}{(t_{2} + 1)} = 400 10 \cdot {t_{2}}^{2} + 10 \cdot t_{2} - 420 = 0 {t_{2}}^{2} + t_{2} - 42 = 0 (t_{2} - 7) (t_{2} + 6) = 0 t_{2} = 7 minutes o r - 6 m i n u t e s$
Given that $t_{2}$ is a natural number, we have, $t_{2} = 7$ minutes
Whereby, $t_{2} = t_{1} - 1,$ we have;
$7 = t_{1} - 1 t_{1} = 1 + 7 = 8 Minutes$
Hence, The trip normally takes $8$ minutes.

Suggest Corrections

Similar questions

Q. a motor boat has two throttle position on its engine . The high speed position propel the boat at 30km/h in still water and the low speed position gives one tired the higher speed . The boat moves from its dock downstream on a river with the throttle at low speed position and return to the dock with throttle at high speed position . The return trip took 5% longer time that it did for the downstream trip . Determine the velocity of flow of river .

A boat moves along the river flow from point A to B and returns back with the same speed. Speed of boat is $N$ times the speed of water. If the speed of water is $1 m / s$ , then the average speed of the boat (in m/s) is

Q. A boat travels with a speed of 15 km/hr in still water. In a river flowing at 5 km/hr, the boat travels some distance downstream and then returns. The ratio of average speed to the speed in still water is

Join BYJU'S Learning Program