The distance between two places is 200 km.; the time taken by motor car from one place to another is less by 2 hrs than the time taken by a zeep car. If the speed of the motor car is 5 km/hr. more than the speed of the zeep car, then by calculating let us write the speed of the motor car
Answers
Answer:
Distance = Rate x Time
From the question we know distance and time.
2:30 = 2.5 hours
D / T = R; therefore; 120 / 2.5 = original rate (speed) = OR
…30 minutes less than 2:30 = 2:00 hours = 2.0 hours
Also from the question we know distance and “new time”
Rate (speed) = Distance / Time
120 / 2.0 = new rate = NR
NR - OR = increase in speed required = your answer in kph
Answer:-
Given:
Distance between two places = 200 km
Let the speed of the zeep car be x km/h.
Given:-
Speed of motor car is 5 km/h more than speed of the zeep car.
→ speed of motor car = (x + 5) km/h.
Also,
Motor car takes 2 hrs less than the zeep car to travel 200 km.
Let the time taken by the zeep car be y hrs.
→ Time taken by motor car = (y - 2) hrs.
We know,
Distance = speed * time.
Hence,
For motor car:
→ 200 = (x + 5) * (y - 2) -- equation (1)
For zeep car:
→ 200 = xy
→ 200/x = y -- equation (2)
Substitute the value of y in equation (1).
→ 200 = (x + 5) * (200/x - 2)
→ 200 = x * (200/x - 2) + 5(200/x - 2)
→ 200 = 200 - 2x + (1000/x) - 10
→ 200 - 200 + 10 = 1000/x - 2x
→ 10 = (1000 - 2x²)/x
→ 10x = 1000 - 2x²
→ 2x² + 10x - 1000 = 0
→ x² + 5x - 500 = 0
→ x² + 25x - 20x - 500 = 0
→ x(x + 25) - 20(x + 25) = 0
→ (x - 20)(x + 25) = 0
• x - 20 = 0
→ x = 20
• x + 25 = 0
→ x = - 25
Speed cannot be negative. So , positive value is taken.
Hence,
- Speed of zeep car = x = 20 km/h
- speed of motor car = x + 5 = 20 + 5 = 25 km/h.
Now,
Substitute the value of x in equation (2).
→ 200/20 = y
→ 10 = y
Hence,
- Time taken by zeep car = y = 10 hours.
- Time taken by motor car = y - 2 = 10 - 2 = 8 hours.
Therefore, the speed of motor car is 25 km/h