Abram and Fred leave opposite ends of a bike trail 8.5 miles apart and travel toward each other. Abram is traveling 3 mph faster than Fred. Find each of their speeds if they meet after 30 mins.

Answer 1

abram and fred, 8.5 miles apart head towards each other, meeting in 30 minutes = 1/2 hour

abram goes 3 mph faster than fred

what are their speeds?

let a=abram's speed

f=fred's speed

a/2 + f/2 = 8.5 speed times time = distance

a=3+f

substitute 2nd equation above into 1st equation above to eliminate one variable

(3+f)/2 +f/2 = 8.5

3+f +f = 17

2f = 17-3 =14

f =14/2 =7 mph = fred's speed

a =7+3 = 10 mph = abram's speed

in half an hour they go 7/2 +10/2 = 3.5+5 = 8.5 miles

in half an hour abram rode 5 miles while fred went just 3 1/2 miles

abram rode 1 1/2 miles more than fred. 5- 3 1/2 = 1 1/2

Answer 2

Distance = (Rate)(Time)

Let x = Fred's rate, then x + 3 = Abram's rate

30 min = 0.5 hours

When they meet, Fred's distance + Abram's distance = 8.5.

So, 0.5x + 0.5(x + 3) = 8.5.

Solve for x.