If a truck travels at 120km to a warehouse with an empty truck. On the return trip, with a full truck, the truck driver travels 20 km slower. If the entire trip took 3.5 hours then determine his speed to the warehouse.
IF the rate is 120 when leaving
and 120-20 is the rate when returning.
v * t=120
(v-20)(3.5-t) = 120
t = 120/v
(v-20)(3.5- 120/v) = 120
3.5 v - 70 - 120 +2400/v = 120
3.5 v^2 - 310 v + 2400 = 0
v = 80 or 8.57
if v = 80
t = 1.5 hours
v = 8.57 does not work
To determine the speed of the truck to the warehouse, we can set up an equation based on the given information.
Let's define:
- x as the speed of the truck to the warehouse
- x - 20 as the speed of the truck returning from the warehouse
To find the time it takes for the truck to travel to the warehouse, we use the formula:
Time = Distance / Speed
Since the distance to the warehouse is the same for both the outbound and return trips, we can set up the equation:
Distance / x + Distance / (x - 20) = 3.5
Given that the initial speed is 120 km/h, we can substitute the distance with the product of the speed and time:
120 * 3.5 / x + 120 * 3.5 / (x - 20) = 3.5
Now we can simplify the equation:
420 / x + 420 / (x - 20) = 3.5
To solve this equation, we can find a common denominator:
420(x - 20) + 420x = 3.5(x)(x - 20)
Now, let's simplify:
420x - 8400 + 420x = 3.5x² - 70x
Combining like terms:
840x - 8400 = 3.5x² - 70x
Rearranging to form a quadratic equation:
3.5x² - 910x + 8400 = 0
Now we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Once we find the roots, we can determine the speed of the truck to the warehouse.