Question

3
henry and blake are both runners. in 4 hours, henry runs 28 miles. in 7 hours, henry runs 49 miles.
the graph below represents the number of miles blake runs in x hours.
blakes running speed
90
80
70
60
distance (miles)
50
40
30
20
10
0 1 2 3 4 5 6 7 8 9
time (hours)
who runs at a slower speed?
a. henry and blake run at the same speed.

b. henry runs at a slower speed.

c. there is not enough information to determine their speed.

d. blake runs at a slower speed.

Explanation:

0,30,40,50,60,70,80,90. The x-axis is 0-9. The red line: at x=5, y=35? No, 35 is between 30 and 40. Wait, maybe the graph is actually showing that at x=5, y=35? But the labels are 0,10,20,30,40,50... So 35 is halfway between 30 and 40. Wait, maybe I made a mistake. Wait, let's calculate Blake's speed correctly. Let's take two points from the graph. Let's take (0,0) and (8,56). Wait, no, the line at x=8 is at y=56? Wait, the graph's top is 90, so at x=8, y=56? No, that doesn't make sense. Wait, maybe the graph is such that the slope is 7. Wait, Henry's speed is 7 mph. Let's check Blake's speed: when x=1, y=7? So speed is 7/1=7. When x=2, y=14? Speed 14/2=7. So Blake's speed is also 7 mph. So Henry and Blake have the same speed. But wait, the options: A is "Henry and Blake run at the same speed." But wait, maybe I misread the graph. Wait, the problem says "the graph below represents the number of miles Blake runs in x hours". Let me re-express:

Henry's speed: 28 miles / 4 hours = 7 mph. 49 miles / 7 hours = 7 mph. So Henry's speed is 7 mph.

Blake's speed: from the graph, let's take x=5 hours, y=35 miles (since the line passes through (5,35) if each square is 5 miles? Wait, no, the y-axis is labeled 0,10,20,30,40,50... So each major tick is 10 miles, with two minor ticks? No, the graph's grid: each square is 10 miles? No, the distance between 0 and 10 is two squares? No, the graph shows that at x=1, y=7? No, that can't be. Wait, maybe the graph is actually a straight line with slope 7. So when x=1, y=7; x=2, y=14; ... x=5, y=35; x=8, y=56. So slope is 7, so speed is 7 mph. So Henry and Blake have the same speed. But wait, the options: A is "Henry and Blake run at the same speed." But let's check the options again.

Wait, maybe I made a mistake. Wait, the graph: let's look at the coordinates. The x-axis is time (hours) from 0 to 9. The y-axis is distance (miles) from 0 to 90. The red line starts at (0,0) and goes through (5,35)? No, 35 is between 30 and 40. Wait, maybe the graph is actually showing that at x=5, y=35, so speed is 35/5=7. At x=8, y=56, speed 56/8=7. So Blake's speed is 7 mph. Henry's speed is also 7 mph. So the answer is A? But wait, the options:

A. Henry and Blake run at the same speed.

B. Henry runs at a slower speed.

C. There is not enough information to determine their speed.

D. Blake runs at a slower speed.

Wait, but according to the calculations, both have speed 7 mph. So the answer is A? But wait, maybe I misread the graph. Wait, maybe the graph's y-axis is 0,7,14,... No, the labels are 0,10,20,... So maybe the graph is scaled differently. Wait, no, the problem says "the graph below represents the number of miles Blake runs in x hours". Let's check the slope again. The slope (speed) is (change in y)/(change in x). Let's take two points: (0,0) and (8,56). Then slope is 56/8=7. So Blake's speed is 7 mph. Henry's speed is 7 mph. So they are the same. So the answer is A.

Wait, but maybe the graph is different. Wait, maybe the line is at x=5, y=35? No, 35 is between 30 and 40. Wait, maybe the graph is actually showing that at x=5, y=35, so 35/5=7. So yes, same speed. So the correct answer is A.

Answer:

A. Henry and Blake run at the same speed.