Samuel was going with 40 km/h and Heather was going with 37 km/h
Step-by-step explanation:
Starting at the same point at the same time, Samuel and Heather rode their bikes in the same direction
We need to find how fast each was going
Assume that Heather's speed is x km/h
∵ Heather's speed = x km/h
∵ Samuel traveled 3 km/h faster than Heather
∴ Samuel's speed = x + 3 km/h
The formula of the distance is distance = speed × time
∵ Samuel travel for 3.5 hours
- Find the distance that Samuel traveled in 3.5 h
∴ Samuel distance = (x + 3) × 3.5
- Multiply the bracket by 3.5 to simplify
∴ Samuel distance = 3.5x + 10.5
∵ Samuel took a break for half hour
∵ Heather kept going
∵ At the end of the break, Heather was 8 km ahead of Samuel
- That means Heather was going for 4 hours (3.5 + 0.5), and her
distance is longer than Samuel distance by 8 km
∴ Heather distance = x × 4 = 4x
- Subtract the distance of Samuel from the distance of Heather
and equate the difference by 8
∵ 4x - (3x + 10.5) = 8
∴ 4x - 3x - 10.5 = 8
- Add the like terms in the left hand side
∴ 0.5x - 10.5 = 8
- Add 10.5 to both sides
∴ 0.5x = 18.5
- Divide both sides by 0.5
∴ x = 37
∵ x represents Heather's speed
∴ Heather's speed = 37 km/h
∵ x + 3 represents Samuel's speed
∴ Samuel's speed = 37 + 3 = 40 km/h
Samuel was going with 40 km/h and Heather was going with 37 km/h
Learn more:
You can learn more about the equation of motion in brainly.com/question/568302
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