Mr. tan makes monthly visits to his parents in Malacca a distance of 240 km from Singapore. he finds that if he increases the average speed by 10km/h, he could save a total of 20min for the journey. find the original speed of Mr. tan.
I have the same question
Well the answer is 80km/hr
Mr. Salazar makes monthly visits to his parents in City M, a distance of 240 km from City N. He finds that if he increases the average speed by 10 km per hour, he can save a total of 20 minutes for the journey. Find the original speed of Mr. Salazar.
To find the original speed of Mr. Tan, we can use the formula:
Speed = Distance / Time
Let's assume Mr. Tan's original speed is "x" km/h. The time taken for the journey at this speed would be:
Time = Distance / Speed
Time = 240 km / x km/h
Now, let's consider the increased speed. Mr. Tan increases his speed by 10 km/h, so his new speed would be "(x + 10)" km/h. With this increased speed, he saves a total of 20 minutes for the journey. We need to convert these minutes to hours for our calculations:
20 minutes = 20 / 60 = 1/3 hours
The time taken for the journey at the increased speed would be:
Time = Distance / Speed
Time = 240 km / (x + 10) km/h
According to the given information, the difference in time between the two speeds is 1/3 hours, so we can set up the equation:
240 km / x km/h - 240 km / (x + 10) km/h = 1/3 hours
Now, let's solve this equation to find the original speed (x) of Mr. Tan.
First, let's simplify the equation by finding the common denominator:
[240(x + 10) - 240x] / x(x + 10) = 1/3
Simplifying further:
[240x + 2400 - 240x] / x(x + 10) = 1/3
2400 / x(x + 10) = 1/3
Cross-multiplying:
3 * 2400 = x(x + 10)
7200 = x^2 + 10x
Rearranging the equation:
x^2 + 10x - 7200 = 0
Now, we can solve this quadratic equation. Using factoring or the quadratic formula, we find that:
(x - 80)(x + 90) = 0
This gives two possible solutions: x = 80 and x = -90.
Since we are considering the speed of Mr. Tan, the solution x = -90 is not valid in this context. Therefore, the original speed of Mr. Tan is 80 km/h.