Yochanan walked from home to the bus stop at an average speed of 5 km / h. he immediately got on his school bus and traveled at an average speed of 60 km / h until he got to school. the total distance from his home to school is 35 km, and the entire trip took 1.5 hours.

5 km walking and 30 km by bus

Step-by-step explanation:

Yochanan walked from home to the bus stop at an average speed of 5 km / h. He immediately got on his school bus and traveled at an average speed of 60 km / h until he got to school. The total distance from his home to school is 35 km, and the entire trip took 1.5 hours. How many km did Yochanan cover by walking and how many did he cover by travelling on the bus?

walking - 5km/h                                         bus - 60km/h

distance walking - d₁                                 distance bus - d₂

time walking - t₁                                         time bus - t₂

d₁ + d₂ = 35

t₁ + t₂ = 1.5

v = d/t

vwalking = d₁/t₁

5 = d₁/t₁ ⇒ d₁ = 5t₁

vbus = d₂/t₂

60 = d₂/t₂ ⇒ d₂ = 60t₂

d₁ + d₂ = 35 ⇒ 5t₁ + 60t₂ = 35

5t₁ + 60t₂ = 35

t₁ + t₂ = 1.5  (*-5)

5t₁ + 60t₂ = 35

-5t₁ -5t₂ = -7.5   (+)

55t₂ = 27.5

t₂ = 27.5/55 = 0.5 h

t₁ + t₂ = 1.5 ⇒ t₁ = 1.5 - 0.5 = 1h

d₁ = 5t₁ ⇒ d₁ = 5.1 = 5 km

d₂ = 60t₂ ⇒ d₂ = 30.0.5 = 30 km