The distance between towns A and B is 280 km.A car and a lorry travel from A to B.The average speed of the lorry is 20km/hr less than that of the car whose speed is x km/hr.The lorry takes 1h and 10 minutes more than the car to travel from A to B.Write an expression in terms of x for the time taken to cover 280km by:a)car b)lorry
speed of car ---- x km/h
speed of lorry -- x-20 km/h
time taken by car = 280/x hrs
time taken by lorry = 280/(x-20) hrs.
1 hour and 10 minutes = 1 + 10/60 = 7/6 hrs
280/(x-20) - 280/x = 7/6
multiply each term by 6x(x-20)
280(6x) - 280(6(x-20)) = 7x(x-20)
expand, arrange as a quadratic and solve using your favourite method.
To find the expressions for the time taken by the car and the lorry to cover the distance between towns A and B, we need to consider the average speed and the extra time taken by the lorry.
Let's start with the car's speed, which is represented by "x" km/hr.
The average speed of the car is x km/hr, so the time taken by the car to cover 280 km can be calculated using the formula: Time = Distance / Speed.
Thus, the expression for the time taken by the car is:
a) Time taken by the car = 280 km / x km/hr
Moving on to the lorry's speed, which is 20 km/hr less than the car's speed.
Therefore, the average speed of the lorry is (x - 20) km/hr.
Now, we know that the lorry takes 1 hour and 10 minutes (which is equal to 70 minutes) more than the car.
To convert this into hours, we divide 70 minutes by 60, which gives us 1.17 hours.
To find the time taken by the lorry to cover 280 km, we add the extra time (1.17 hours) to the time taken by the car to travel the same distance.
The expression for the time taken by the lorry is:
b) Time taken by the lorry = (280 km / (x - 20) km/hr) + 1.17 hours