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
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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