a motorist travels regularly between two towns. he usually takes 5 hrs when traveling at a certain speed,he finds out that if he increases his average speed by 15km/hr the journey takes one hour less. find his total speed
Let's assume the motorist's usual speed is 's' km/hr.
According to the given information, when the motorist travels at speed 's', the journey takes 5 hours. This can be represented as:
Distance = Speed * Time
d = 5s ...(1)
Now, when the motorist increases his speed by 15 km/hr, his new speed becomes 's + 15' km/hr. The journey now takes 1 hour less than before, which means it takes 4 hours. This can be represented as:
Distance = Speed * Time
d = 4(s + 15) ...(2)
Since the distances covered in both cases are the same (the motorist is traveling between the same two towns), we can equate equations (1) and (2):
5s = 4(s + 15)
5s = 4s + 60
5s - 4s = 60
s = 60
Therefore, the motorist's usual speed is 60 km/hr.
To find his total speed, we add the increase in speed of 15 km/hr to his usual speed:
Total speed = 60 km/hr + 15 km/hr = <<60+15=75>>75 km/hr.
Hence, his total speed is 75 km/hr.
Let's denote the motorist's usual speed as \( x \) km/hr.
According to the given information, when the motorist travels at the usual speed, it takes 5 hours to travel between the two towns.
When the motorist increases their speed by 15 km/hr, their new speed becomes \( x + 15 \) km/hr, and the journey takes 1 hour less than before.
Using the formula \( \text{time} = \frac{\text{distance}}{\text{speed}} \), we can write the following equations based on the given information:
For the usual speed:
\[ 5 = \frac{\text{distance}}{x} \]
For the increased speed:
\[ 4 = \frac{\text{distance}}{x + 15} \]
To find the total speed, we need to add the usual speed and the increase in speed:
\[ \text{Total speed} = x + (x + 15) \]
To solve the equations, we can equate the distance traveled in both cases:
\[ \text{distance} = \text{distance} \]
\[ 5x = 4(x + 15) \]
Simplifying the equation:
\[ 5x = 4x + 60 \]
\[ x = 60 \]
So, the motorist's usual speed is 60 km/hr.
To find the total speed:
\[ \text{Total speed} = x + (x + 15) \]
\[ \text{Total speed} = 60 + (60 + 15) \]
\[ \text{Total speed} = 60 + 75 \]
\[ \text{Total speed} = 135 \]
Therefore, the motorist's total speed is 135 km/hr.