Problem 7. The two trains travel for the same amount of time, but
because their speeds are different, they travel different distances. The
two distances add to 450 miles.
distance = speed * time
For the commuter train, you have distance d1, time t, and speed s. For the express train, you have distance d2, time t, and speed s + 25.
The time is 6 hours, so, For the commuter train, you have distance d1, time 6, and speed s. For the express train, you have distance d2, time 6, and speed s + 25.
d = st
Commuter: d1 = st
Express d2 = (s + 25)t
Add the equations: d1 + d2 = st + (s + 25) t d1 + d2 = st + st + 25t d1 + d2 = 2st + 25t d1 + d2 = (2s + 25)t
The two distances add to 450 miles, d1 + d2 = 450, and t = 6.
450 = (2s + 25)(6)
75 = 2s + 25
50 = 2s
s = 25
The commuter train's speed is 25 mph. The express train's speed is 50 mph.
Check: distance = speed * time In 6 hours, the commuter train travels d = 25 mph * 6 hours = 150 miles. In 6 hours, the express train travels 50 mph * 6 hours = 300 miles. 150 miles + 300 miles = 450 miles. The distances do add to 450 miles and the speed of the express train is 25 mph faster, so our answer is correct.
The slope will be the same for a straight line no matter which two points you pick as you know. All you need to do is to calculate the difference in the y coordinates of the 2 points and divide that by the difference of the x coordinates of the points(rise over run). That will give you the slope.
