Mr Ernst leaves home at noon, traveling at 50 mph. His loving wife leaves at 1 pm with a briefcase that Mr. Ernst forgot. How fast must his wife drive to catch him by 5 pm?
d1 = 50mi/h * 1h + 50mi/h * 4h = 250 mi
d2 = r*t = 250 mi
r*4 = 250
r = 62.5 mi/h = Wife's speed.
To find out how fast Mrs. Ernst must drive to catch up with Mr. Ernst by 5 pm, we need to determine the time it would take for Mrs. Ernst to catch up to him.
Mr. Ernst started traveling at noon, so by 5 pm, he would have been on the road for a total of 5 hours. Mrs. Ernst, on the other hand, started traveling at 1 pm, so she would be traveling for a total of 4 hours.
We know that the distance covered by both Mr. and Mrs. Ernst must be the same when they meet. This is because they are traveling on the same road. Therefore, we can use the equation Distance = Speed × Time to find the speed Mrs. Ernst needs to catch up with her husband.
Let's assume that Mrs. Ernst needs to travel at a speed of x mph to catch up with Mr. Ernst. Since Distance = Speed × Time, we can write the equation:
Distance covered by Mr. Ernst = Distance covered by Mrs. Ernst
From the equation, we can derive the following equation:
50 mph × 5 hours = x mph × 4 hours
Now, we can solve for x to determine the speed Mrs. Ernst needs to travel:
250 miles = 4x
Dividing both sides of the equation by 4:
x = 250 miles / 4 hours
Simplifying:
x = 62.5 mph
Therefore, Mrs. Ernst needs to travel at a speed of 62.5 mph to catch up with Mr. Ernst by 5 pm.