travelling at 90km/hr except for a 30 minute rest stop. Average speed for the trip is 78km/hr.
what is the total travelling time and what is the total distance travelled??
thanks
Let D = distance traveled (km)
T = total time of trip in hours
90 (T-0.5) = D
D = 78 T
Two equations, two unknowns.
Solve by substitutuion.
90(T - 0.5) = 78 T
12 T = 45
T = 3.75 hours (3.25 of which was driving)
D = 292.5 km
To find the total traveling time and total distance traveled, we can use the formula:
Average Speed = Total Distance / Total Time
Given that the average speed for the trip is 78 km/hr, we can substitute this value into the formula.
78 km/hr = Total Distance / Total Time
Now let's find the total distance traveled:
Since the distance traveled during the rest stop is zero, we can exclude it from the calculation.
Let's assume the time taken for the trip without the rest stop is represented by 't' hours. So, the total time for the trip including the rest stop will be 't + 30 minutes'.
Now, we can set up an equation:
90 km/hr * t hr + 0 km/hr * 0.5 hr = Total Distance
Simplifying the equation, we get:
90t + 0 = Total Distance
90t = Total Distance
Now, let's plug this value into the previous equation:
78 km/hr = 90t / (t + 30/60)
To solve for t, we can cross-multiply:
78t + 78*(30/60) = 90t
Let's solve for t:
78t + 39 = 90t
39 = 12t
t = 39/12
t = 3.25 hours
Now that we have the value of 't', we can substitute it back into one of the previous equations to find the total distance:
Total Distance = 90t
Total Distance = 90 * 3.25
Total Distance = 292.5 km
Therefore, the total traveling time is 3.25 hours (or 3 hours and 15 minutes) and the total distance traveled is 292.5 kilometers.