A motorist has to travel 3.50 km in a city with an average speed not exceeding 25 km/h. If the average speed increases to 40 km/h, find the time he will gain in his journey.
d = V*T = 3.50 km
T = 3.50/V = 3.50/25 = 0.14 h.
T = 3.50/40 = 0.0875 h.
0.14 - 0.0875 = 0.0525 h = 3.15 Min. gained.
To find the time gained by the motorist in his journey, we need to calculate the time it takes to travel the given distance at both average speeds and then compare the two.
First, let's calculate the time it takes to travel 3.50 km at an average speed of 25 km/h:
Time = Distance / Speed
Time1 = 3.50 km / 25 km/h = 0.14 hours
Next, let's calculate the time it takes to travel the same distance at an average speed of 40 km/h:
Time2 = 3.50 km / 40 km/h = 0.0875 hours
To find the time gained, we subtract the time taken at the faster speed from the time taken at the slower speed:
Time gained = Time1 - Time2
Time gained = 0.14 hours - 0.0875 hours = 0.0525 hours
Therefore, the motorist will gain approximately 0.0525 hours in his journey when the average speed increases from 25 km/h to 40 km/h.
To find the time the motorist will gain in his journey, we need to compare the time taken to travel the distance at the two different average speeds.
First, let's calculate the time taken to travel 3.50 km at an average speed of 25 km/h:
Time taken = Distance / Speed
= 3.50 km / 25 km/h
To simplify the calculation, let's convert the units to the same system. We can convert km/h to m/s by dividing the speed by 3.6:
Speed in m/s = 25 km/h / 3.6
= 6.94 m/s
Now we can calculate the time taken:
Time taken = Distance / Speed
= 3.50 km / 6.94 m/s
Next, let's calculate the time taken to travel the same distance at an average speed of 40 km/h:
Speed in m/s = 40 km/h / 3.6
= 11.11 m/s
Time taken = Distance / Speed
= 3.50 km / 11.11 m/s
Now we can compare the two times to find the time the motorist will gain:
Time gained = Time taken at 25 km/h - Time taken at 40 km/h
Substituting the values:
Time gained = (3.50 km / 6.94 m/s) - (3.50 km / 11.11 m/s)
Calculating this expression will give us the time the motorist will gain in his journey.