b) Two families Mäkinen* and Nieminen* travel by cars a distance of 185 km. In the middle of the
travel both have a break of 20 min. During driving family Nieminen has an average speed of 90 km/h.
Family Mäkinen drives the first part at an average speed of 70 km/h. What average speed would
family Mäkinen need for the rest of the travel in order to get to the destination at the same time with
family Nieminen.
* Mäkinen and Nieminen are examples of two very common Finnish family names.
Nieminen has to travel a distance of (185/2)km at 90km/hr = 1.02777 hours to go.
If your statement means that Mäkinen also drove halfway before stopping, then they took 1.3214 hours, so they have to drive 185/2 km in 2*1.02777-1.3214 = 0.734 hours, or 126 km/hr.
On the other hand, maybe you meant that both took a break at the same time, when Mäkinen had not yet gone halfway. Adjust the needed speed in that case.
To find the average speed that family Mäkinen would need for the rest of the travel in order to reach the destination at the same time as family Nieminen, we can use the formula:
Average Speed = Total Distance / Total Time
First, we need to calculate the total time taken by family Nieminen to travel the distance of 185 km. We know that their average speed is 90 km/h, so we can use:
Total Time taken by family Nieminen = Total Distance / Average Speed
= 185 km / 90 km/h
Next, we need to calculate the time taken by family Mäkinen for the first part of the travel, where they drove at an average speed of 70 km/h. Let's call this time "T1".
T1 = Distance / Speed
T1 = (185 km / 2) / 70 km/h [divided by 2 because they took a break in the middle]
T1 = 92.5 km / 70 km/h
T1 = 1.3214 hours
Since both families will reach the destination at the same time, the total time taken by family Mäkinen must be the same as the total time taken by family Nieminen. Therefore, the total time taken by family Mäkinen is:
Total Time taken by family Mäkinen = Total Time taken by family Nieminen
Total Time taken by family Mäkinen = 185 km / 90 km/h
Now, we can determine the time taken by family Mäkinen for the rest of the travel, let's call this time "T2".
T2 = Total Time taken by family Mäkinen - T1
T2 = (185 km / 90 km/h) - 1.3214 hours
Finally, we can find the average speed that family Mäkinen would need for the rest of the travel, using the formula:
Average Speed = Total Distance / Total Time
Average Speed = (185 km / 2) / T2
By plugging in the values, we can calculate the average speed that family Mäkinen would need for the rest of the travel to reach the destination at the same time as family Nieminen.