A motorist travelling at a steady speed of 120km/h covers a section of the highway in 30min. After a speed limit is imposed he finds that when travelling at the maximum speed allowed he takes 20 min. longer than before to cover the same section.
Calculate the speed limit.
If he travels at 120 Km per hour in 30'(ie 1/2 hour) he did 120/2=60Km.
If he travels at max speed allowed he takes 30+20=50'or 50/60=5/6 hours to reach his destination. so speed is: 60/(5/6)= 360/5=72Km/h
To solve this problem, we can let "x" be the original time it took to cover the section before the speed limit was imposed.
According to the problem, the motorist traveled at a steady speed of 120 km/h for x minutes, covering the section. This can be expressed as:
Distance = Speed x Time
Distance = 120 km/h * (x/60) h
After the speed limit is imposed, the motorist took 20 minutes (or 1/3 hour) longer to cover the same section. So the new time would be (x + 1/3) hours.
According to the problem, the motorist was traveling at the maximum speed allowed during this time. Let's call this speed limit "v". So the distance covered would be:
Distance = v km/h * ((x + 1/3)/60) h
Since the distance covered is the same in both cases, we can set up the equation:
120 km/h * (x/60) h = v km/h * ((x + 1/3)/60) h
We can now solve this equation to find the speed limit "v".
First, let's simplify the equation:
120x = vX + v/3
Now let's solve for v by isolating the variable:
vX = 120x - v/3
vX = 120x - (1/3)v
Next, let's factor out the v:
v(X + 1/3) = 120x
Now we can solve for v by dividing both sides by (X + 1/3):
v = 120x / (X + 1/3)
We know that the speed limit v cannot be greater than or equal to 120 km/h, as the motorist took longer to cover the same section. Therefore, we can assume that v is less than 120 km/h.
By substituting x = 30 minutes (or 0.5 hours) into the equation, we can find the value of v:
v = 120 * 0.5 / (0.5 + 1/3)
v = 60 / (0.5 + 1/3)
v = 60 / (0.5 + 0.3333)
v = 60 / 0.8333
v ≈ 71.9984 km/h
Therefore, the speed limit is approximately 72 km/h.
To calculate the speed limit, we need to find the difference in time it takes the motorist to cover the section of the highway before and after the speed limit is imposed. Given that the motorist initially covers the section in 30 minutes at a speed of 120 km/h, and after the speed limit is imposed, it takes 20 minutes longer to cover the same section.
Let's break down the problem and calculate the distance covered in both scenarios:
Distance covered when travelling at 120 km/h:
Time = 30 minutes = 30/60 = 0.5 hours
Speed = 120 km/h
Distance = Speed × Time = 120 km/h × 0.5 hours = 60 km
Distance covered when travelling at the maximum speed allowed:
Time = 30 minutes + 20 minutes = 50 minutes = 50/60 = 5/6 hours
Distance = Speed × Time
Now, we can calculate the speed limit by equating the distances covered in both scenarios. Let's assign the speed limit as 'x':
Speed when travelling at the maximum speed limit = x km/h
Distance = Speed × Time = x km/h × (5/6) hours
Since the distances covered in both scenarios are equal, we can set up the equation:
60 km = x km/h × (5/6) hours
To solve for x, we can cross multiply:
60 km * 6/5 = x km/h
Simplifying, we get:
72 km = x km/h
Therefore, the speed limit is 72 km/h.