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
- Samuel traveled 3 km/h faster than Heather
- After 3.5 h Samuel stopped for a half-hour break, but Heather kept going
- Heather was 8 km ahead of Samuel
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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and
are like terms as they contain the same variable
raised to the same power.