two people, john and mary, are 200 miles apart and leave at the same time to meet. They are driving toward each other at constant rate on the same straight road. John is traveling at 45 mph and Mary is traveling at 35 mph. When they meet, how many miles will they be from john's house?
rate * time = distance
45t + 35t = 200
80t = 200
t = 2.5 hours
45 * 2.5 = ?
90,5
To find out how many miles they will be from John's house when they meet, we need to determine how long it will take for them to meet first.
We can use the formula: Time = Distance / Speed
Let's calculate the time it will take for John and Mary to meet:
For John:
Distance = 200 miles
Speed = 45 mph
Time taken by John = Distance / Speed = 200 miles / 45 mph
Similarly, for Mary:
Distance = 200 miles
Speed = 35 mph
Time taken by Mary = Distance / Speed = 200 miles / 35 mph
Since they both left at the same time, the times taken by both John and Mary will be the same.
Now, we can add the times for John and Mary to find the total time taken for them to meet:
Total time taken = Time taken by John + Time taken by Mary
Substituting the values:
Total time taken = (200 miles / 45 mph) + (200 miles / 35 mph)
Now that we have the total time taken, we can find out how far John will be from his house when they meet.
Distance traveled by John = Speed * Time taken by John
Substituting values:
Distance traveled by John = 45 mph * (200 miles / 45 mph)
Simplifying:
Distance traveled by John = 200 miles
So when John and Mary meet, John will be 200 miles away from his house.