for the following write an equation and solve it.
Terri and Nick rode their bikes toward each other starting from two towns 24 miles apart. Terri rode three miles per hour faster than Nick and they met in two hours. How fast did each person ride?
I think I need to use the formula d=rt
terri speed=3+nickspeed
terridistance+nickdistance=24
terrispeed*2hrs + nickdistnace*2hrs=24mi
(Nickspeed+3)*2hrs+nickdistance(2)=24
solve for nickspeed first.
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: Ashwin and Donald decided to set out from two towns on their bikes, which are 247 miles apart, connected by a straight Roman road in England. When they finally met up somewhere between the two towns, Ashwin had been cycling for 9 miles a day. The number of days for the whole adventure is 3 more than the number of miles that Donald had been cycling in a day. How many miles did each cycle? explanatory solutions
Yes, you're on the right track! In this problem, you can use the formula d = rt, where d represents the distance, r represents the rate (or speed), and t represents time.
Let's set up the equation for Terri and Nick:
For Terri:
d = rt
For Nick:
d = (r - 3)t
Since they are riding toward each other, the sum of their distances will equal the total distance between the towns, which is 24 miles. So we have:
d + d = 24
Now, substitute the expressions for distance for Terri and Nick into the equation:
rt + (r - 3)t = 24
Next, we can simplify the equation:
rt + rt - 3t = 24
2rt - 3t = 24
At this point, we have a linear equation. To solve for r, we need to isolate the variable on one side.
2rt - 3t = 24
t(2r - 3) = 24
Divide both sides of the equation by (2r - 3):
t = 24 / (2r - 3)
Since we know t = 2 (as they met in two hours), we can substitute this value into the equation:
2 = 24 / (2r - 3)
Now we can solve for r:
2(2r - 3) = 24
4r - 6 = 24
4r = 30
r = 30 / 4
r = 7.5
So Terri rode at a speed of 7.5 miles per hour. To find Nick's speed, substitute r = 7.5 back into one of the original equations.
d = rt
24 = (7.5 - 3)t
24 = 4.5t
t = 24 / 4.5
t = 5.33
So Nick rode at a speed of approximately 5.33 miles per hour.