distance and time application problem

Question

2 campers leave a place at the same time

one travels north at 10km/h faster than the other, which is traveling south

after 3 hours, the campers are 420 km apart

find their speeds

Answer 1

Two campes, A and B leave the camp site, mark 0, at the same time.

 

Camper A travels at speed x km/h

Camper B travels at speed y km/h

Relationship between campers speed, Camper A travels 10 km/h faster than Camper B, therefore y = 10 + x

 

After 3 hours, Camper A has traveled m km away from point 0

After 3 hours, Camper B has traveled n km away from point 0

Relationship between campers distance, Camper A is 420 km away from Camper B, therefore m + n = 420

 

Distance traveled by Camper A in 3 hours, m, = 3x

Distance traveled by Camper B in 3 hours, n, = 3y

Therefore 3x + 3y = 420

 

Equation 1: y = 10 + x

Equation 2: 3x + 3y = 420

 

Use substitution method to solve equation:

3x + 3(10+x) = 420

3x + 30 + 3x = 420

6x + 30 = 420

6x = 390

x = 65

y = 10+ 65 = 75

 

Camper A travels 65 km/h

Camper B travels 75 km/h