Question

HELP ME

Henry took 5 hours to travel from Town A to Town B. His average speed for the whole journey was 70 km/h. For the first 3/7 of the journey, he traveled at a speed of 60 km/h. What is his speed for the remaining journey?

Answer 1

Let's denote the speed for the remaining journey as "x" km/h. We know that Henry's average speed for the entire journey was 70 km/h. Using the concept of average speed, we can calculate it based on the two segments of the journey.

The first segment, which is 3/7 of the journey, was at a speed of 60 km/h.

The second segment, which is the remaining part of the journey (1 - 3/7 = 4/7), is at a speed of "x" km/h.

We can use the formula for average speed, which is the total distance divided by the total time:

Average Speed = Total Distance / Total Time

We know that the average speed is 70 km/h, and the total time is 5 hours. To find the total distance, we need to consider both segments of the journey:

Total Distance = (Distance of the First Segment) + (Distance of the Second Segment)

The distance can be calculated using the formula Distance = Speed × Time.

For the first segment, the distance is (3/7) of the total distance:

Distance of the First Segment = (3/7) × Total Distance

For the second segment, the distance is (4/7) of the total distance:

Distance of the Second Segment = (4/7) × Total Distance

Now, let's set up the equations and solve for "x":

Average Speed = Total Distance / Total Time

70 km/h = [(3/7) × Total Distance + (4/7) × Total Distance] / 5 hours

Now, we'll simplify the equation:

70 = [(3/7 + 4/7) × Total Distance] / 5

70 = (7/7) × Total Distance / 5

Now, we can simplify further:

70 = (1) × Total Distance / 5

70 = Total Distance / 5

To find the total distance, multiply both sides by 5:

Total Distance = 70 × 5

Total Distance = 350 km

Now that we know the total distance is 350 km, we can find the speed for the remaining journey:

Distance of the Second Segment = (4/7) × Total Distance

Distance of the Second Segment = (4/7) × 350 km

Distance of the Second Segment = 200 km

Now, we can find the speed for the remaining journey using the formula Distance = Speed × Time:

200 km = x km/h × (Time for the Second Segment)

Time for the Second Segment can be calculated as:

Time for the Second Segment = (Distance of the Second Segment) / x

Time for the Second Segment = 200 km / x

We know that the total time for the journey was 5 hours, so:

5 hours = (Time for the First Segment) + (Time for the Second Segment)

5 hours = [(3/7) × Total Distance] / 60 km/h + [(4/7) × Total Distance] / x km/h

Now, we can plug in the values:

5 hours = [(3/7) × 350 km] / 60 km/h + [(4/7) × 350 km] / x km/h

Simplify:

5 hours = (150/7) hours + (200/7) hours / x km/h

Now, combine the fractions:

5 hours = (350/7) hours / x km/h

To isolate x, multiply both sides by x:

5 hours * x km/h = 350/7 hours

Now, divide both sides by 5 hours to solve for x:

x km/h = (350/7 hours) / (5 hours)

x km/h = (70/7)

x km/h = 10 km/h

So, Henry's speed for the remaining journey is 10 km/h.

Answer 2

100km/h

Explanation:

To find Henry's speed for the remaining journey, we can use the formula for average speed:

Average Speed = Total Distance / Total Time

Henry traveled from Town A to Town B with an average speed of 70 km/h and took 5 hours. This means he covered a distance of 70 km/h * 5 hours = 350 km for the entire journey.

For the first 3/7 of the journey, he traveled at 60 km/h. To find the distance covered during this portion of the journey, we can calculate:

Distance1 = (3/7) * 350 km = 150 km

The remaining distance for the remaining journey is:

Remaining Distance = Total Distance - Distance1 = 350 km - 150 km = 200 km

Now, we can find his speed for the remaining journey:

Speed = Distance / Time

Speed = 200 km / (5 hours - the time for the first part of the journey)

Henry's speed for the remaining journey is:

Speed = 200 km / (5 hours - 3 hours) = 200 km / 2 hours = 100 km/h

So, his speed for the remaining journey is 100 km/h.