Answer:
The first car reaches its destination in 6 hours.
Step-by-step explanation:
Speed of the first car = 50 miles per hour
Time taken = t hours
Distance travelled = Speed × Time = 50 t
Speed of the second car = 60 miles per hour
Time taken = [tex](t-1)[/tex] hours
Distance travelled = Speed × Time = [tex]60(t-1)[/tex]
As two cars travel the same distance,
[tex]50t=60(t-1)\\50t=60t-60\\60=60t-50t\\60=10t\\t=\frac{60}{10}\\t=6[/tex]
So, the first car reaches its destination in 6 hours.
It would take the first car 6 hours to reach its destination.
Speed is the ratio of distance to time. It is given by:
Speed = distance /time
Since the two cars travel at the same distance, let d represent this distance.
The first car travel at 50 miles per hour and reaches its destination at t hours. Hence:
50 = d / t
d = 50t (1)
The second car travels at a rate of 60 miles per hour and reaches its destination 1 hour earlier than the first car. Hence the time = t - 1. Hence:
60 = d / (t - 1)
d = 60(t - 1)
d = 60t - 60 (2)
Equating both equations gives:
50t = 60t - 60
10t = 60
t = 6 hours
Hence it would take the first car 6 hours to reach its destination
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