2 friends are 60 miles apart. They decide to ride thier bicycles to meet each other. Sally starts from the college and heads east,riding at a rate of 21 mph.At the same time Teresa starts from the river and heads west, riding at a rate of 15 mph. How far does each cyclist ride in t hours? When the cyclists meet, what must be true about the ditances they have ridden? Write and solve an equation to find when they meet.
How far did they travel in t hours?
t= distance/speed
The distance when they mey? Wont the two riders distances add to 60 miles?
This is a newer verion of a problem that is usually stated with trains.
Using distance = rate*time with time = 1hr you can see they've ridden 21 and 15 miles respectively. When they meet they should've covered the 60mi between them, correct?
Suppose they meet after time t hours of cycling, whatever time that may be. Can you see that this is somewhere between 1 and 2 hours of cycling? After 2hrs of cycling they will have met and passed each other. At time t hr they've traveled 21*t + 15*t = 60mi. Can you solve for t?
To find how far each cyclist rides in t hours, we can use the formula distance = rate × time.
Sally's rate is 21 mph, so her distance is 21 × t miles.
Teresa's rate is 15 mph, so her distance is 15 × t miles.
When the cyclists meet, their combined distances must add up to 60 miles since they started 60 miles apart.
So, the equation to solve for when they meet is:
21t + 15t = 60
Combining like terms, we get:
36t = 60
To isolate t, we divide both sides of the equation by 36:
t = 60 / 36
Simplifying, we find:
t = 5/3 or approximately 1.67 hours.
Therefore, each cyclist will have ridden approximately:
Sally's distance: 21 × (5/3) = 35 miles.
Teresa's distance: 15 × (5/3) = 25 miles.