Question

A worker drives to work each morning, always leaving at the same time. When he drives at

an average speed of 30km/hr he arrives six minutes early, but when he drives at an average
speed of 20km/hr he arrives six minutes late. What is the distance between his house and his
office? Calculate his average speed when he arrives precisely on time. Explain your answer.

Answer 1

Step-by-step explanation:

speed = distance/time

distance/speed = distance / distance/time = time

when we define the equations, we must be careful to use the same scales as in the given numbers.

as we are dealing with km/h for speed, we need to have distance measured in km, and time in hours.

6 minutes is therefore 1/10 of an hour (1 hour = 60 minutes).

distance/30 = x - 1/10

distance/20 = x + 1/10

we subtract equation 2 from equation 1 :

distance/30 = x - 1/10

- distance/20 = x + 1/10

-----------------------------------

distance/30 - distance/20 = -2/10

we multiply by 60 to eliminate all fractions :

2×distance - 3×distance = -2×6 = -12

-distance = -12

distance = 12 km

x = the travel time to arrive on time.

distance/30 = x - 1/10

12/30 = x - 1/10

12 = 30x - 3

15 = 30x

x = 15/30 = 0.5 hours = 30 minutes

so, he has half an hour for his 12 km trip to work to arrive precisely on time.

that means his average speed for that must be

12/0.5 = 24/1 = 24 km/h