A car travelled a distance of (2x+13) km at 67,5 km/h and (5x-20) km at 72 km/h. If the total time for the entire journey was 90 minutes, find the value of x.

Answer 1

Let's first calculate the time it took to travel the first distance:

Time = Distance / Speed
Time = (2x + 13) / 67.5

Next, let's calculate the time it took to travel the second distance:

Time = Distance / Speed
Time = (5x - 20) / 72

Since the total time for the entire journey was 90 minutes, we can write the equation:

(2x + 13) / 67.5 + (5x - 20) / 72 = 90/60

Simplify the equation:

(2x + 13) / 67.5 + (5x - 20) / 72 = 1.5

Multiply everything by 67.5 and 72 to eliminate the fractions:

72(2x + 13) + 67.5(5x - 20) = 1.5 * 67.5 * 72

Expand and simplify:

144x + 936 + 337.5x - 1350 = 6075
481.5x - 414 = 6075
481.5x = 6489

Now, divide by 481.5 to solve for x:

x = 13.47

Therefore, the value of x is 13.47.