Joe wants to ﬁnd out how far it is across the lake. His boat has a speedometer but no odometer. The table shows the boats velocity at 10 second intervals. Estimate the distance across the lake Using right-end point values. $$\begin{array} { c | c }
\begin{array} { c }
\text { Time } \
( \mathrm { sec } )
\end{array} & \begin{array} { c }
\text { Velocity } \
( \mathrm { ft } / \mathrm { sec } )
\end{array} \
\hline 0 & 0 \
10 & 12 \
20 & 30 \
30 & 57 \
40 & 54 \
50 & 59 \
60 & 56 \
70 & 59 \
80 & 49 \
90 & 15 \
100 & 0
\end{array}$$
A) 5900 ft
B) 391 ft
C) 3910 ft
D) 4010 ft

Question

Joe wants to ﬁnd out how far it is across the lake. His boat has a speedometer but no odometer. The table shows the boats velocity at 10 second intervals. Estimate the distance across the lake Using right-end point values. $$\begin{array} { c | c } 
\begin{array} { c } 
\text { Time } \
( \mathrm { sec } )
\end{array} & \begin{array} { c } 
\text { Velocity } \
( \mathrm { ft } / \mathrm { sec } )
\end{array} \
\hline 0 & 0 \
10 & 12 \
20 & 30 \
30 & 57 \
40 & 54 \
50 & 59 \
60 & 56 \
70 & 59 \
80 & 49 \
90 & 15 \
100 & 0
\end{array}$$
A) 5900 ft
B) 391 ft
C) 3910 ft
D) 4010 ft

Quizplus · Accepted Answer

To estimate the distance across the lake using right-end point values, we can look at the last velocity value at 100 seconds, which is 0 ft/sec. We can then add up the distances traveled during each time interval using the velocity from the previous time interval. For example, during the interval from 90-100 seconds, the boat traveled 10 seconds at a velocity of 15 ft/sec, so the distance traveled during that interval is 10 x 15 = 150 ft. Adding up all the distances, we get:

10 x 12 = 120
10 x 30 = 300
10 x 57 = 570
10 x 54 = 540
10 x 59 = 590
10 x 56 = 560
10 x 59 = 590
10 x 49 = 490
10 x 15 = 150
Total distance = 3870 ft

Using right-end point values means that we are underestimating the distance traveled during each time interval, so the actual distance across the lake will be greater than our estimate. The answer closest to our estimate is C) 3910 ft.

Joe Wants to ﬁNd Out How Far It Is Across