Any help with the following would be greatly appreciated. I don't understand how to use the information given to create the equation.
1) A car travels between A and B at an average speed of 60 km/h. If the car increased its
average speed to 100 km/h it would take 10 minutes less to make the trip. How far is it
between the towns?
2) Car A is travelling along a freeway at 100 km/h when it is passed by car B. If both cars
maintain a constant speed and the end of the freeway is 10 km away, find the speed at
which car B must travel to beat car A to the end of the freeway by 1 minute.
1) You start with the definition of average speed.
avg speed= distance/time
60km/hr= 1km/min= distanceab/time
distanceab= 1km/min*time
but also
distanceab= 100km/60min*(time-10)
set these two equations equal, solve for time, then, find distance from the original equation.
2) distance= speed*time
10km= 100km60min*time
10km= speedB*(time-1)
again, set them equal, solve for time, then solve speedB
Sure, I'd be happy to help you understand how to create the equations for both of these problems.
1) Let's start with the first problem. We are given that a car travels between point A and point B at an average speed of 60 km/h. If the car increases its average speed to 100 km/h, it would take 10 minutes less to make the trip. We need to find the distance between points A and B.
To solve this problem, let's first assign variables. Let's say the distance between A and B is d kilometers.
We know that the first leg of the trip is done at a speed of 60 km/h and the second leg is done at a speed of 100 km/h. We also know that the time difference between these two legs is 10 minutes, or 1/6 hours.
Using the formula distance = speed * time, we can create two equations to represent this situation:
For the first leg: d = 60 * t1, where t1 is the time taken for the first leg.
For the second leg: d = 100 * t2, where t2 is the time taken for the second leg.
We can also represent the time difference between the legs with an equation:
t2 = t1 - 1/6
Now, we have a system of equations with two unknowns (d and t1). We can solve this system of equations to find the value of d.
2) Moving on to the second problem, we are given that Car A is travelling along a freeway at 100 km/h when it is passed by Car B. The end of the freeway is 10 km away, and we need to find the speed at which Car B must travel to beat Car A to the end of the freeway by 1 minute.
Let's say the speed of Car B is v km/h. We know that Car A is travelling at 100 km/h.
We can use the formula distance = speed * time, where the distance is 10 km, to create two equations for the travel time for each car:
For Car A: 10 = 100 * t1
For Car B: 10 = v * t2
We also know that the difference in travel time between the two cars is 1 minute, or 1/60 hours:
t1 - t2 = 1/60
Again, we have a system of equations with two unknowns (v and t1). We can solve this system of equations to find the value of v.
I hope this helps you understand how to create the equations for these problems. Let me know if you have any further questions!