Yochanan walked from home to the bus stop at an average speed of 5km/h. He immediately got on his school bus and traveled at an average speed of 60km/h until he got to school. The distance from his home to school is 35 kilometers, and the entire trip took 1.5 hours. How many kilometers did Yochanan cover by walking and how many kilometers did he cover by travelling on the bus?
distance by bus --- x km
distance walking -- 35-x km
x/5 + (35-x)/60 = 1.5
times 60
12x + 35-x = 90
11x = 55
x = 5
he walked 5 km, and went 30 km by bus
check:
time walking = 5/5 = 1 hr
time on bus = 30/60 = 1/2 hr
total is 1.5 hrs
To find out how many kilometers Yochanan covered by walking and how many kilometers he covered by traveling on the bus, we need to use the information provided.
Let's assume that Yochanan covered x kilometers by walking and (35 - x) kilometers by traveling on the bus.
We are given that Yochanan's average speed while walking was 5 km/h. Therefore, the time taken to walk the distance x kilometers can be calculated as x/5 hours.
We are also given that Yochanan's average speed on the bus was 60 km/h. Therefore, the time taken to travel the distance (35 - x) kilometers on the bus can be calculated as (35 - x)/60 hours.
The total time taken for the entire trip is given as 1.5 hours. So, we can set up the following equation:
x/5 + (35 - x)/60 = 1.5
To solve this equation, we can multiply through by the least common multiple (LCM) of 5 and 60, which is 60:
60*(x/5) + 60*((35 - x)/60) = 60*1.5
Simplifying, we get:
12x + 35 - x = 90
Combining like terms, we obtain:
11x + 35 = 90
Subtracting 35 from both sides, we have:
11x = 55
Dividing both sides by 11, we find:
x = 5
Now, we know that Yochanan covered 5 kilometers by walking and (35 - 5) = 30 kilometers by traveling on the bus.