A word problem.
David flew 300km on a commuter plane, then 2000km on a passenger jet. The passenger jet flew twice as fast as the commuter plane. The total flying time for the journey was 3.25 hours. What was the speed of each plane, in kilometers per hour?
Please help. I've been trying to tackle this problem for an hour+ and had no luck solving it.
let the speed of the commuter plane be x km/h
then the speed of the passenger jet is 2x km/h
300/x + 2000/2x = 3.25
300/x + 1000/x = 3.25
1300/x = 3.25
3.25x = 1300
x = 1300/3.25 = 400
so ......
To solve this word problem, we can use a system of equations. Let's assign variables to represent the speeds of the two planes.
Let's call the speed of the commuter plane "x" km/h.
The speed of the passenger jet is given as twice the speed of the commuter plane, so it is 2x km/h.
Now, let's set up an equation based on the given information about the total flying time:
The time taken to fly 300km on the commuter plane can be calculated using the formula time = distance/speed. So, the time taken for this part of the journey is 300/x hours.
The time taken to fly 2000km on the passenger jet can be calculated using the same formula. So, the time taken for this part of the journey is 2000/(2x) hours.
According to the problem, the total flying time for the journey is 3.25 hours. So, we set up the equation:
300/x + 2000/(2x) = 3.25
To solve this equation, we can clear the fractions by multiplying through by 2x:
2(300) + 2000 = 3.25(2x)
600 + 2000 = 6.5x
2600 = 6.5x
Now, we can solve for x by dividing both sides of the equation by 6.5:
2600/6.5 = x
400 = x
So, the speed of the commuter plane is 400 km/h.
Since the speed of the passenger jet is given as twice the speed of the commuter plane, the speed of the passenger jet is 2(400) = 800 km/h.
Therefore, the speed of the commuter plane is 400 km/h, and the speed of the passenger jet is 800 km/h.
Sure, let's break down the problem step by step to find the solution.
Let's consider the speed of the commuter plane as "x" km/h. Since the passenger jet is twice as fast as the commuter plane, its speed is "2x" km/h.
Now, we need to use the information given to create an equation based on the time it took to complete the journey.
First, let's calculate the time it took for the commuter plane to fly 300km. The formula for time is distance divided by speed:
Time taken by the commuter plane = 300 km / x km/h
Time taken by the commuter plane = 300/x hours
Next, let's calculate the time it took for the passenger jet to fly 2000km:
Time taken by the passenger jet = 2000 km / 2x km/h
Time taken by the passenger jet = 1000/x hours
The total flying time for the journey is given as 3.25 hours:
Total time = 3.25 hours
Now, we can create an equation by adding the time taken by the commuter plane and the time taken by the passenger jet and setting it equal to the total flying time:
300/x + 1000/x = 3.25
To solve this equation, we can multiply both sides by x to eliminate the denominators:
300 + 1000 = 3.25x
1300 = 3.25x
To find the value of x, we need to divide both sides of the equation by 3.25:
x = 1300 / 3.25
x = 400
So, the speed of the commuter plane is 400 km/h. Since the passenger jet is twice as fast, its speed is 2 times 400, which is 800 km/h.
Therefore, the speed of the commuter plane is 400 km/h and the speed of the passenger jet is 800 km/h.