GOING SKIING. LEON DROVE 270 MILES TO THE LODGE IN THE SAME TIME AS PAT DROVE 330 MILES TO THE LODGE. IF PAT DROVE 10 MILES PER HOUR FASTER THAN LEON, THEN HOW FAST DID EACH OF THEM DRIVE?
I REALLY NEED HELP ON THIS ONE. PLEASE! IF YOU CAN SHOW THE WORK WILL BE GREAT I THINK I WILL UNDERSTAND IT BETTER THAN JUST SEEING THE ANSWER. tHINKS
Leon's travel time = (270 miles/V1)Pat's travel time = (330 miles/V2)
The times are equal.
V1 = Leon's speed and V2 = Pat's speed
V2 = V1 + 10
270/V1 = 330/(V1 + 10)
(V1 +10)/V1 = 330/270 = 11/9
1 + (10/V1) = 11/9
10/V1 = 2/9
V1 = 45 mph
V2 = 55 mph
. Leon drove 270 miles to the lodge in the same time as Pat drove 330 miles to lodge. If Pat drove 10miles per hour faster than Leon, then how fast did each of them drive?
b.Why are there usually two solutions in quadratic equations?
c.under what situation would one or more solutions of a rational equation be unacceptable?
I think pat was the faster one that's my inser
I have looked at this question several times and it seems as though there is missing information to solve this problem.Without time, you can not rate speed.Yes it tells the difference in milage and speed difference but I bellieve this question has no answer without a key pice of information such as departure and arival time of atleast one person. I have seen many people post questions such as these and try to throw you off to make you thump your gray matter so you will assume there is a answer, when in all reality there is none.But perhaps I am just missing somthing and have not approached this question in the right light but the way I see it there are unlimited answers to this question since there ahs been no reffrence point given for time elapsed.If there is a correct answer,I would be very anxious to here it so I could figure out the formula used to calculate this. Good luck!!!
I apologize for any confusion. Let's go through the problem step by step.
Given:
- Leon drove 270 miles to the lodge and Pat drove 330 miles to the lodge.
- Pat drove 10 miles per hour faster than Leon.
- We need to find the speeds at which Leon and Pat drove.
To start, let's assign variables to the unknowns:
- Let V1 represent Leon's speed.
- Let V2 represent Pat's speed.
We are given that Pat drove 10 miles per hour faster than Leon, so we can write:
V2 = V1 + 10
We are also given that Leon drove 270 miles to the lodge in the same time as Pat drove 330 miles to the lodge. We can set up a time equation:
Time taken by Leon = Time taken by Pat
To find the time taken by each person, we can use the formula: Time = Distance / Speed
- For Leon: Time taken by Leon = 270 / V1
- For Pat: Time taken by Pat = 330 / V2
Since the times are equal, we have the equation:
270 / V1 = 330 / V2
Now, let's substitute V2 with V1 + 10:
270 / V1 = 330 / (V1 + 10)
To solve this equation, we can cross-multiply:
270 * (V1 + 10) = 330 * V1
Expand both sides:
270V1 + 270 * 10 = 330V1
Combine like terms:
270V1 + 2700 = 330V1
Now, let's isolate the V1 terms by subtracting 270V1 from both sides:
2700 = 330V1 - 270V1
Simplify:
2700 = 60V1
Divide both sides by 60:
2700 / 60 = V1
Simplify:
45 = V1
So, Leon's speed, V1, is 45 mph.
To find Pat's speed, V2, we can use the equation V2 = V1 + 10:
V2 = 45 + 10
V2 = 55 mph
Therefore, Leon drove at a speed of 45 mph, and Pat drove at a speed of 55 mph.
I hope this explanation helps! Let me know if you have any further questions.