How Do You Calculate Travel Time and Distance with Stops and Varying Speeds?

[rafael_josem]

Help, can't solve this problem...

Hi, I have the follwing problem and I don't know how to start...

A person make a trip in car with an average speed of 89.5km/h, except when the person stops 22 mins to rest. If the average speed of the person is 77.8km/h, How much time the person spends on the trip? How far the person goes?


Thanks...

 

[WalterContrata]

Hello Rafael,

Can you write 2 equations for the trip time (T), one equation from the first sentence of the problem, and one from the second?

Hope this helps,
Walter

 

[quicknote]

Hi there,

I understand that you are having trouble solving this problem. It is important to first define the variables in the problem. In this case, the average speed of the person is given as 89.5km/h, but we also know that the person stops for 22 minutes during the trip. This means that the average speed is not constant throughout the entire trip.

To solve this problem, we can use the formula: Distance = Speed x Time. We know that the total distance traveled is equal to the average speed multiplied by the total time spent on the trip. However, since the average speed is not constant, we need to break the trip into two parts - the time spent driving at 89.5km/h and the time spent resting at 0km/h.

Let's call the time spent driving at 89.5km/h as t1 and the time spent resting as 22 minutes or 0.367 hours. We can then set up the following equation: Distance = (89.5km/h x t1) + (0km/h x 0.367h). We can simplify this to Distance = 89.5t1.

Next, we know that the average speed for the entire trip is 77.8km/h, which means that the total distance traveled is also equal to (77.8km/h x total time). We can set up another equation: Distance = 77.8 x total time.

Now, we have two equations for distance, so we can set them equal to each other: 89.5t1 = 77.8 x total time. We also know that the total time is equal to the time spent driving (t1) plus the time spent resting (0.367h). We can substitute this into the equation: 89.5t1 = 77.8(t1 + 0.367).

Solving for t1, we get t1 = 0.622 hours. This is the time spent driving at 89.5km/h. To find the total time, we add the time spent resting (0.367h) to this, giving us a total time of 0.989 hours.

To find the total distance traveled, we can plug in the value of t1 into the equation Distance = 89.5t1. This gives us a distance of 55.7km.

Therefore, the person spent 0.989