Question
A boat is navigating a river with a current speed of 2
km/h. It takes the boat 75 minutes longer to cover a distance of 56 km upstream than it does to cover 45 km downstream. Additionally, the boat travels upstream for 90 minutes and downstream for 110 minutes. Determine the total distance covered by the boat.Solution
Let the speed of the boat in still water = 'x' km/h Then, upstream and downstream speed of the boat are (x - 2) km/h and (x + 2) km/h, respectively According to the question, {56/(x - 2)} - {45/(x + y)} = (75/60) Or, (56x + 112 - 45x + 90) ÷ (x2 - 4) = 1.25 Or, 11x + 202 = 1.25x2 - 5 Or, 1.25x2 - 11x - 207 = 0 Or, 5x2 - 44x - 828 = 0 Or, 5x2 - 90x + 46x - 828 = 0 Or, 5x(x - 18) + 46(x - 18) = 0 Or, (5x + 46)(x - 18) = 0 So, x = 18 (since speed cannot be negative). Therefore, upstream and downstream speed of the boat is 16 km/h and 20 km/h Total distance travelled = 16 X (90/60) + 20 X (110/60) = 24 + (110/3) = (182/3) km
‘A’ and ‘B’ started moving towards each other at same time with a speed of 27 km/hr and 9 km/hr, respectively. If the dis...
A train covers a certain distance at a speed of 24 km/h and the next same distance with a speed of 42 km/h and the next same distance with a speed of 72...
Train ‘A’ running with a speed of 54 km/hr. can cross a standing goods train of 4 times its length in 20 seconds. Find the time taken by 240 meters ...
Vikas covered a certain distance by bike. If he covers 40% of the distance at 40 km/h, 50% of the distance at 25 km/h and the remaining 10% distance at ...
- The speed ratio of Renu and Meenu is 4:5, respectively. Renu travels a distance of 300 km from point 'A' to 'B', while Meenu covers the same distance but i...
- In a 200-metre race, runner A can give runner B a 20-metre head start and still finish at the same time. Similarly, runner B can give runner C a 10-metre h...
- Nikita covered a total distance of 400 km — partly by airplane at 200 km/h and partly by bus at 80 km/h. If she took 3.5 hours to reach, how many kilomet...
‘A’ and ‘B’ started moving towards each other at same time with a speed of 22 km/hr and 14 km/hr, respectively. If the distance covered by ‘A�...
Ajay and Vishal left the place ‘X’ with different speeds which are in the ratio 9:5 respectively. Ajay left the place 36 seconds after Vishal. If af...
A boy goes to school at 9 km/Hr and return at a speed of 8 km/hr. If he takes 17 hrs in all. Find the distance from his village to school?
