if the speed of a car is increased from 90km/h to 120km/h, the time is reduced by one hour to reach the destination. Calculate the distance between the two towns.
let the distance be d km
time at 90 km/h ---- d/90
time at 120 km/h --- d/120
d/90 - d/120 = 1
solve for d
hint: multiply each term by 360 to clear fractions
Let's assume the original distance between the two towns is "d" kilometers.
At a speed of 90 km/h, the time it takes to cover the distance is given by the formula:
Time = Distance / Speed
So, when traveling at 90 km/h, the time taken is d / 90.
Now, at a speed of 120 km/h, the time taken to cover the distance is given by:
Time = Distance / Speed
So, when traveling at 120 km/h, the time taken is d / 120.
According to the given information, the time is reduced by one hour when the speed is increased from 90 km/h to 120 km/h.
So, we can write the equation:
(d / 90) - (d / 120) = 1
To solve this equation, we need to find a common denominator for 90 and 120. The lowest common multiple of 90 and 120 is 360.
Multiplying all terms by 360, we have:
4d - 3d = 360
Simplifying, we get:
d = 360
Therefore, the distance between the two towns is 360 kilometers.
To solve this problem, we can use the formula:
Time = Distance / Speed
Let's assume that the distance between the two towns is represented by 'd'.
1. First, let's calculate the time it takes to travel at the initial speed of 90 km/h:
Time1 = Distance / Speed1
Time1 = d / 90
2. Now, let's calculate the time it takes to travel at the increased speed of 120 km/h:
Time2 = Distance / Speed2
Time2 = d / 120
3. We are given that the time is reduced by one hour, so we can set up the equation:
Time2 = Time1 - 1
Substituting the values of Time1 and Time2 into the equation, we get:
d / 120 = d / 90 - 1
4. To simplify the equation, let's get rid of the fractions by multiplying both sides by the lowest common denominator, which is 360:
3d = 4d - 360
5. Now, let's isolate the 'd' term:
d = 360
Therefore, the distance between the two towns is 360 kilometers.