how far can a boy ride his bicycle if he rides away at 10 km per hour and returns at 9 km per hour? the entire trip takes 9.5.
time = distance/speed, so if the distance is x,
x/10 + x/9 = 9.5
now just find x
To find out how far the boy can ride his bicycle, we need to calculate the distance he covered while riding away and the distance he covered while returning.
Let's assume the distance he rides away is "x" km.
The time taken to ride away can be found by dividing the distance by the speed:
Time taken to ride away = x km / 10 km per hour = x/10 hours
Similarly, the distance he covers while returning is also "x" km.
The time taken to return can be found by dividing the distance by the speed:
Time taken to return = x km / 9 km per hour = x/9 hours
According to the given information, the entire trip takes 9.5 hours. So, the total time can be represented as:
Total time = Time taken to ride away + Time taken to return
Therefore, we can write the equation as:
x/10 + x/9 = 9.5
To solve this equation:
Step 1: Multiply the entire equation by 90 (LCM of 10 and 9) to eliminate the denominators:
9x + 10x = 9.5 * 90
Step 2: Simplify:
19x = 855
Step 3: Divide both sides by 19 to isolate x:
x = 855 / 19
x ≈ 45 km
Therefore, the boy can ride his bicycle approximately 45 km before turning back.
To find the distance the boy can ride his bicycle, we can use the formula:
Distance = Speed × Time
Let's assume the distance the boy travels at 10 km/hr is "x" km.
The time taken to travel x km at 10 km/hr is x/10.
Since the boy travels back at 9 km/hr, the time taken to travel the same x km at 9 km/hr is x/9.
According to the given information, the entire trip takes 9.5 hours. So we have the equation:
x/10 + x/9 = 9.5
To solve this equation, we can find a common denominator and cross-multiply:
9x + 10x = 10 × 9.5
19x = 95
x = 95/19
x = 5
Therefore, the boy can ride his bicycle for a distance of 5 kilometers.